Math3 Derivative and IntegralLaajuus (3 cr)
Code: TZLM3300
Credits
3 op
Teaching language
- Finnish
- English
Responsible person
- Anne Rantakaulio, TKN
- Antti Kosonen, TER, TRY, TRM
- Ida Arhosalo, TSA, TAR
- Harri Varpanen, TIC
- Pekka Varis, TTV
- Kalle Niemi, TLS, TLP
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Enrollment
18.11.2024 - 09.01.2025
Timing
10.03.2025 - 30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV24S1Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 10.3. and 30.4.2025
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2025
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
10.03.2025 - 30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV24S2Tieto- ja viestintätekniikka (AMK)
-
ZJATTV24S2Avoin amk, Tieto- ja viestintätekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 10.3. and 30.4.2025
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2025
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
10.03.2025 - 30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV24S3Tieto- ja viestintätekniikka (AMK)
-
ZJATTV24S3Avoin amk, Tieto- ja viestintätekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 10.3. and 30.4.2025
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2025
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2024 - 09.01.2025
Timing
10.03.2025 - 27.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA24SR1Insinööri (AMK), sähkö- ja automaatiotekniikka, päivätoteutus
-
ZJATSA24S1Avoin amk, Sähkö-ja automaatiotekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot auditoriossa + laskuharjoitukset tietokoneluokasssa viikoilla 11-17
Läpäisykoe Exam-studiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Läpäisykoe Exam-studiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2024 - 09.01.2025
Timing
10.03.2025 - 27.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA24SR2Insinööri (AMK), sähkö- ja automaatiotekniikka, päivätoteutus
-
ZJATSA24S1Avoin amk, Sähkö-ja automaatiotekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot auditoriossa + laskuharjoitukset tietokoneluokasssa viikoilla 11-17
Läpäisykoe Exam-studiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Läpäisykoe Exam-studiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
03.03.2025 - 27.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
TIC24S1Bachelor's Degree Programme in Information and Communications Technology
-
ZJATIC24S1Avoin amk,ICT, Information and Communication Technology, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Further information for students
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
03.03.2025 - 30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
TIC24S2Bachelor's Degree Programme in Information and Communications Technology
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Further information for students
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2024 - 09.01.2025
Timing
03.03.2025 - 27.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TAR24S1Bachelor's Degree Programme in Automation and Robotics
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-15, exam on week 16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
10.02.2025 - 30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 79
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Groups
-
TKN24SMKonetekniikka (AMK)
-
TKN24SAKonetekniikka (AMK)
-
TKN24SBKonetekniikka (AMK)
-
ZJATKN24SMAvoin amk, Konetekniikka, Monimuoto
-
ZJATKN24S1Avoin amk, Konetekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
27.01.2025 - 25.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 60
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Kalle Niemi
Scheduling groups
- TRY24SA (Capacity: 35. Open UAS: 0.)
- TRY24B (Capacity: 35. Open UAS: 0.)
Groups
-
TRY24S1Rakennus- ja yhdyskuntatekniikka (AMK)
-
ZJATRY24S1Avoin amk, Rakennus- ja yhdyskuntatekniikka, Päivä
Small groups
- TRY24SA
- TRY24B
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 27.1. and 25.4.2025
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2025
Student workload
The estimated workload is 81 hours
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
If a student enrolled in the course does not show activity within three weeks of the start of the course, the enrollment will be rejected.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
27.01.2025 - 06.05.2025
Number of ECTS credits allocated
3 op
Virtual portion
1.5 op
Mode of delivery
50 % Face-to-face, 50 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS24KMMLogistiikka - tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevään aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Lisäksi iltawebinaareja kevään aikana. Kokeet loppukeväästä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla. Läpäisykoe on Exam-studiossa.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Timing
13.01.2025 - 18.05.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ville Kotimäki
Groups
-
TER24S1Energia- ja ympäristötekniikka (AMK)
-
ZJATER24S1Avoin amk, Energia- ja ympäristötekniikka , päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Learning materials and recommended literature
Kurssilla käytetään opettajan jakamaa PDF-materiaalia.
Teaching methods
Kurssi koostuu luennoista ja laskuharjoitusten laskemisesta.
Exam dates and retake possibilities
Tenttien aikataulut ilmoitetaan ensimmäisellä luennolla.
Student workload
40 h kontaktiopetusta
5 h kokeita
36 h itsenäistä opiskelua
Further information for students
Arviointi tehdään laskuharjoitusten ja kaksiosaisen loppukokeen perusteella.
Lisäksi kurssilla on päiväopiskelijoita koskeva läsnäolovelvoite (80% oppitunneista on oltava paikalla).
Opintojakson ensimmäinen tehtävä tulee tehdä kolmen viikon kuluessa toteutuksen alkamisesta. Tehtävän tekemättä jättäneet poistetaan toteutukselta.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
18.11.2024 - 09.01.2025
Timing
13.01.2025 - 19.05.2025
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
10 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on vuodenvaihteessa ja kurssi suoritetaan kevään aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Läpäisykoe on Exam-studiossa. Arvosanakokeita järjestetään loppukeväästä. Arvosanakokeet mahdollisesti Exam-studiossa tai etävalvotusti tiettyinä ajankohtina. Tarkemmat yksityiskohdat/ajankohdat ilmoitetaan työtilassa toteutuksen alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information for students
Arvosana 1: Pakollisia harjoitustehtäviä ja läpäisykoe hyväksytysti
Arvosanat 2-5: Pakollisia harjoitustehtäviä, läpäisykoe hyväksytysti, lisäksi arvosanat 2-5 perustuvat arvosanakokeen pisteisiin.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2024 - 09.01.2025
Timing
13.01.2025 - 18.05.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ville Kotimäki
Groups
-
TER24SMEnergia- ja ympäristötekniikka (AMK)
-
ZJATER24SMAvoin amk, Energia- ja ympäristötekniikka, monimuoto
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Learning materials and recommended literature
Kurssilla käytetään opettajan jakamaa PDF-materiaalia.
Teaching methods
Kurssi koostuu luennoista ja laskuharjoitusten laskemisesta.
Exam dates and retake possibilities
Tenttien aikataulut ilmoitetaan ensimmäisellä luennolla.
Student workload
16 h kontaktiopetusta
5 h kokeita
60 h itsenäistä opiskelua
Further information for students
Arviointi tehdään laskuharjoitusten ja kaksiosaisen loppukokeen perusteella.
Opintojakson ensimmäinen tehtävä tulee tehdä kolmen viikon kuluessa toteutuksen alkamisesta. Tehtävän tekemättä jättäneet poistetaan toteutukselta.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2024 - 22.08.2024
Timing
09.09.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 58
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Scheduling groups
- TLS23SA (Capacity: 35. Open UAS: 0.)
- TLS23SB (Capacity: 35. Open UAS: 0.)
Groups
-
TLS23S1Logistiikka - tutkinto-ohjelma (AMK)
Small groups
- TLS23SA
- TLS23SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot/laskuharjoitukset 2h/vko viikoilla 37-50
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Loppukoe(arvosanakoe) kurssin viimeisellä luentokerralla (vko 50). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla. Läpäisykoe Exam-studiossa itselle sopivaan ajankohtaan ennen arvosanakoetta.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2024 - 22.08.2024
Timing
02.09.2024 - 08.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
20 - 44
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Groups
-
TLP24VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP23S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 2.9. - 8.12.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examissa viikolta 48 lähtien, arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Student workload
Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Virtual portion
1.5 op
Mode of delivery
50 % Face-to-face, 50 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
20 - 25
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS23SMMLogistiikka - tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 31.12.2024
Number of ECTS credits allocated
3 op
Virtual portion
2.5 op
Mode of delivery
17 % Face-to-face, 83 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA24KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
-
ZJATSA24KMAvoin amk, Sähkö- ja automaatiotekniikka, Monimuoto
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.04.2024 - 30.04.2024
Timing
01.05.2024 - 30.09.2024
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on huhtikuussa ja kurssi suoritetaan kesän aikana. Kurssilla on aktivoiduttava toukokuun kahden ensimmäisen viikon aikana tai ilmoittautuminen hylätään. Toukokuussa järjestetään ohjauswebinaareja, joille osallistuminen ei ole pakollista. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa.
Kesäopinnot/IT-instituutin opiskelijat (20 paikkaa).
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokeeseen ilmoittautumista.
Toukokuussa järjestetään ohjauswebinaareja, jossa käydään arvosanan 1 kriteereiden tasolla kurssin aiheita läpi.
Exam dates and retake possibilities
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Ne sijoittuvat elo- ja syyskuulle. (Pelkän läpäisykokeen, jolla voi saada korkeintaan arvosanan 1, voi tehdä jo aikaisemmin. Sen voi tehdä Exam-studiossa Exam-studion aukioloaikojen puitteissa.)
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S1Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 4.3. and 26.4.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S2Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 4.3. and 26.4.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S3Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 4.3. and 26.4.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
TTV23S5Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 4.3. and 26.4.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
TTV23SMTieto- ja viestintätekniikka (AMK)
-
ZJATTV23SMAvoin amk, Tieto- ja viestintätekniikka, Monimuoto
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 4.3. and 26.4.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC23S1Bachelor's Degree Programme in Information and Communications Technology
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Further information for students
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TAR23S1Bachelor's Degree Programme in Automation and Robotics
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-15, exam on week 16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA23SR1Sähkö- ja automaatiotekniikka (AMK)
-
TSA23SR2Sähkö- ja automaatiotekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
12.02.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Kalle Niemi
Scheduling groups
- TRY23SA (Capacity: 35. Open UAS: 0.)
- TRY23SB (Capacity: 35. Open UAS: 0.)
Groups
-
TRY23S1Rakennus- ja yhdyskuntatekniikka (AMK)
-
ZJATRY23S1Avoin amk, Rakennus- ja yhdyskuntatekniikka, Päivä
Small groups
- TRY23SA
- TRY23SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 8.1. - 15.3.2024
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
05.02.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 94
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Groups
-
TKN23SBKonetekniikka (AMK)
-
ZJATKN23S1Avoin amk, Konetekniikka, Päivä
-
ZJATKN23SMAvoin amk, Konetekniikka, Monimuoto
-
TKN23SMKonetekniikka (AMK)
-
TKN23SAKonetekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 5.2. - 30.4.2024.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examissa viikolta 14 lähtien, arvosanakoe ja monimuotojen läpäisykoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Alternative completion methods
Web-based course in Summer 2024
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 07.01.2024
Timing
08.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 20
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Loppukokeita järjestetään loppukeväästä. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 20.05.2024
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Face-to-face, 66 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS23KMMLogistiikka - tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevään aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppukeväästä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
01.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ville Kotimäki
Groups
-
ZJATER23S1Avoin amk, Energia- ja ympäristötekniikka , päivä
-
TER23S1Energia- ja ympäristötekniikka (AMK)
-
TER23SMEnergia- ja ympäristötekniikka (AMK)
-
ZJATER23SMAvoin amk, Energia- ja ympäristötekniikka , monimuoto
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
16.10.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA23KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on syksyn alussa ja kurssi suoritetaan syksyn aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Loppukokeita järjestetään loppusyksystä. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Face-to-face, 66 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS22SMMLogistiikka - tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Kalle Niemi
Scheduling groups
- TLS22SA (Capacity: 30. Open UAS: 0.)
- TLS22SB (Capacity: 30. Open UAS: 0.)
Groups
-
TLS22S1Logistiikka - tutkinto-ohjelma (AMK)
Small groups
- TLS22SA
- TLS22SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 30.10. - 17.12.2023.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Extra material in Applied Calculus (http://www.opentextbookstore.com/details.php?id=14)
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Final exam in week 45, resit 1 in week 47 and resit 2 in week 2/2024.
Alternative completion methods
Web-based course in Spring and Summer 2024
Student workload
Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h
Further information for students
Continuous feedback: automated tests and returnable tasks
Final exam
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Groups
-
TLP22S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
TLP23VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 30.10. - 17.12.2023.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examissa viikolta 48 lähtien, arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Student workload
Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.04.2023 - 30.04.2023
Timing
01.05.2023 - 31.08.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on huhtikuussa ja kurssi suoritetaan kesän aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Ne sijoittuvat viikoille 32-35.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 6.3.2023 and 21.4.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
ZJATTV22SMAvoin amk, Tieto- ja viestintätekniikka, Monimuoto
-
TTV22SMTieto- ja viestintätekniikka (AMK)
-
TTV22SM2Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 6.3.2023 and 28.4.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
TTV22S1Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevätlukukauden 2023 toinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam dates and retake possibilities
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information for students
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat3 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC22S1Bachelor's Degree Programme in Information and Communications Technology
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Further information for students
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
ZJATTV22S2Avoin amk, Tieto- ja viestintätekniikka, Päivä
-
TTV22S2Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevätlukukauden 2023 toinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam dates and retake possibilities
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information for students
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat3 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV22S3Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 6.3. and 21.4.2023
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
TTV22S5Tieto- ja viestintätekniikka (AMK)
-
ZJATTV22S5Avoin amk, Tieto- ja viestintätekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 6.3.2023 and 28.4.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV22S4Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
The course is implemented between 6.3. and 21.4.2023
Learning materials and recommended literature
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam dates and retake possibilities
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Alternative completion methods
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information for students
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Pekka Varis
Groups
-
TSA22SR2Sähkö- ja automaatiotekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Sirpa Alestalo
Teacher in charge
Ida Arhosalo
Groups
-
ZJATSA22S1Avoin amk, Sähkö- ja automaatiotekniikka, Päivä
-
TSA22SR1Sähkö- ja automaatiotekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot/laskuharjoitukset 2*2/vko viikoilla 10-16
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Loppukoe viikolla 16. Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Kurssista löytyy myös itsenäisesti tehtävä verkkototeutus. Jos kontaktiopetukseen ei halua osallistua, kannattaa ilmoittautua verkkototeutukselle.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information for students
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvän läpäisytestin. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista. Jotta läpäisytestiin ja arvosanakokeeseen voi osallistua, täytyy opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) olla hyväksytysti tehty.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
21.11.2022 - 05.01.2023
Timing
06.03.2023 - 30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TAR22S1Bachelor's Degree Programme in Automation and Robotics
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-15, exam on week 16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 05.01.2023
Timing
09.01.2023 - 26.02.2023
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Face-to-face, 66 % Online learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Groups
-
TER22S1Energia- ja ympäristötekniikka (AMK)
-
TER22SMEnergia- ja ympäristötekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
This course is implemented 23.1.2023 - 2.4.2023 instead of the previously announced 9.1.2023 - 26.2.2023.
Lectures will be streamed online.
Guided exercises will be held at campus or online depending on the implementation of your degree programme.
Learning materials and recommended literature
Written material, video material and exercises prepared by teacher.
Appropriate textbooks in Finnish:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.
Teaching methods
Lectures, guided exercises, independent work, exams
Exam dates and retake possibilities
Exam to pass the course will be done independently during the course in e-exam studio or as a more traditional supervised exam during week 8, depending on the implementation of your degree programme.
The grade-determining exam will take place during week 8.
First resit 22.3.2023
Second resit 12.4.2023
Alternative completion methods
Face-to-face and online implementations are available in spring and in autumn. It is also possible to attend the course online during summer 2023.
Student workload
For six weeks:
Lectures 2 * 45 min
Exercises (depending on programme): 3 * 45 min or 2 * 45 min
Additionally:
Exams approximately 4 h
Independent work approximately 55 - 60 h
Content scheduling
Themes will be discussed in the following order (one week / theme):
1. Definition of the Derivative
2. Symbolic Differentiation
3. Applications of the Derivative
4. Definition of the Integral and Symbolic Integration
5. The Fundamental Theorem of Calculus
6. Applications of Integration
Further information for students
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 19.05.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on vuodenvaihteessa ja kurssi suoritetaan kevään aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Loppukokeita järjestetään viikoilla 8-17. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TRY22SA (Capacity: 35. Open UAS: 0.)
- TRY22SB (Capacity: 35. Open UAS: 0.)
Groups
-
ZJATRY22S1Avoin amk, Rakennus- ja yhdyskuntatekniikka, Päivä
-
TRY22S1Rakennus- ja yhdyskuntatekniikka (AMK)
Small groups
- TRY22SA
- TRY22SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 20.2. - 28.4.2023.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisy- ja arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Alternative completion methods
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 21.05.2023
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLS22KMMLogistiikan tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevään aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppukeväästä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
01.01.2023 - 21.05.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 100
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Groups
-
TKN22SAKonetekniikka (AMK)
-
TKN22SBKonetekniikka (AMK)
-
ZJATKN22SMAvoin amk, Konetekniikka, Monimuoto
-
TKN22S1Konetekniikka (AMK)
-
TKN22SMKonetekniikka (AMK)
-
ZJATKN22S1Avoin amk, Konetekniikka, Päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 20.2. - 28.4.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisy- ja arvosanakoe viikolla 17, sen uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Alternative completion methods
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
05.09.2022 - 18.11.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Pasi Lehtola
Groups
-
TSA22KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 5.9. - 18.11.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, assignments, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, assignments, exam.
Exam dates and retake possibilities
Läpäisy- ja arvosanakoe viikolla 46. Uusintakoe 1 viikolla 49 ja uusintakoe 2 viikolla 2.
Alternative completion methods
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 28 h
Independent work 53 h
Further information for students
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 14.10.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Scheduling groups
- TLS21SA (Capacity: 35. Open UAS: 0.)
- TLS21SB (Capacity: 35. Open UAS: 0.)
Groups
-
TLS21S1Logistiikan tutkinto-ohjelma (AMK)
Small groups
- TLS21SA
- TLS21SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot/laskuharjoitukset 2*2/vko viikoilla 35-41
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Loppukoe kurssin viimeisellä luentokerralla (vko 41). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Alternative completion methods
Kurssista löytyy myös itsenäisesti tehtävä verkkototeutus. Jos kontaktiopetukseen ei halua osallistua, kannattaa ilmoittautua verkkototeutukselle.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 21.12.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen on elokuussa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Voit osallistua viikolla 41 loppukokeeseen Rajakadulla, muut loppukokeet myöhemmin syksyllä valvotaan etäyhteydellä. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Loppukokeita järjestetään viikoilla 41-49. Viikon 41 kokeet on Rajakadulla luokassa. Viikoilla 43-49 järjestetään 3 etävalvottua koetta.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 31.10.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLP22VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP21S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 35-40, exam on week 41.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
TTV21S1Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevätlukukauden 2022 toinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam dates and retake possibilities
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information for students
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
ZJA21STIPPTVAvoin amk, tekniikka, Tieto-ja viestintätekniikka, päivä
-
TTV21S2Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Kevätlukukauden 2022 toinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam dates and retake possibilities
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information for students
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV21S3Tieto- ja viestintätekniikka (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Opintojakso toteutetaan viikoilla 11 - 17 (14.3. - 29.4.2022) Lutakon kampuksella kontaktina Dynamolla tai etänä Zoomissa
Learning materials and recommended literature
Opintojakson pääasiallisena materiaalina toimivat opettajan jakama kirjallinen materiaali sekä videomateriaali verkko-oppimisympäristössä.
Opintojaksoon liittyvä suositeltava kirjallisuus:
- Lehtola, Rantakaulio - Tekninen matematiikka 2
Teaching methods
Kontaktiopetus 3+2 h /viikko, ohjatut laskuharjoitukset, itsenäinen työskentely
Exam dates and retake possibilities
Opintojakson tarkempi aikataulu sovitaan opintojakson aloitustapaamisessa ja julkaistaan verkko-oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Opintojakson laskennallinen kuormitus on 3op * 27h/op = 81h.
Kontaktiopetus noin 35h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 20h
Further information for students
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvä läpäisytesti. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta läpäisytestiin ja kokeeseen voi osallistua, täytyy opintojakson kotitehtävät ja välitestit olla suoritettuna hyväksytysti.
Avoin AMK 10 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV21S5Tieto- ja viestintätekniikka (AMK)
-
ZJA21STIPPTVAvoin amk, tekniikka, Tieto-ja viestintätekniikka, päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Opintojakso toteutetaan viikoilla 11 - 17 (14.3. - 29.4.2022) Lutakon kampuksella kontaktina Dynamolla tai etänä Zoomissa
Learning materials and recommended literature
Opintojakson pääasiallisena materiaalina toimivat opettajan jakama kirjallinen materiaali sekä videomateriaali verkko-oppimisympäristössä.
Opintojaksoon liittyvä suositeltava kirjallisuus:
- Lehtola, Rantakaulio - Tekninen matematiikka 2
Teaching methods
Kontaktiopetus 3+2 h /viikko, ohjatut laskuharjoitukset, itsenäinen työskentely
Exam dates and retake possibilities
Opintojakson tarkempi aikataulu sovitaan opintojakson aloitustapaamisessa ja julkaistaan verkko-oppimisympäristössä.
Alternative completion methods
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Opintojakson laskennallinen kuormitus on 3op * 27h/op = 81h.
Kontaktiopetus noin 35h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 20h
Further information for students
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvä läpäisytesti. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta läpäisytestiin ja kokeeseen voi osallistua, täytyy opintojakson kotitehtävät ja välitestit olla suoritettuna hyväksytysti.
Avoin AMK 10 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 110
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Kalle Niemi
Groups
-
TTV21SMTieto- ja viestintätekniikka (AMK)
-
ZJA21STPMTVAvoin amk, tekniikka, Tieto- ja viestintätekniikka, verkko
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Opintojakso toteutetaan 7.3.2022 - 30.4.2022.
Learning materials and recommended literature
Luentomoniste ja harjoitustehtävät Moodlessa.
Teaching methods
Verkkoluennot ja -ohjaus, itsenäinen työskentely ja verkkotyöskentely.
Practical training and working life connections
Kurssin sisältö pyritään kytkemään työelämässä esiintyviin ongelmiin.
Exam dates and retake possibilities
Kurssin tenttikäytänteet ilmoitetaan kurssin ensimmäisellä tapaamiskerralla.
Alternative completion methods
Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.
Student workload
Itsenäistä opiskelua 81 h
Further information for students
Opintojakso arvioidaan kokeen tai kokeiden ja laskuharjoituksista kerättävien pisteiden perusteella.
Avoin AMK verkko-opinnot 20 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
ZJA21STPICAvoin amk, tekniikka, Information and Communications Technology, päivä
-
TIC21S1Bachelor's Degree Programme in Information and Communications Technology
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Two lessons (90min) per week during weeks 10-16.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Practical training and working life connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Alternative completion methods
Times of the exams will be given in the first lesson of the course.
Further information for students
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 22.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TRY21SA (Capacity: 30. Open UAS: 0.)
- TRY21SB (Capacity: 30. Open UAS: 0.)
Groups
-
TRY21S1Rakennus- ja yhdyskuntatekniikka (AMK)
-
ZJA21STPPRYAvoin amk, tekniikka, Rakennus- ja yhdyskuntatekniikka, päivä
Small groups
- TRY21SA
- TRY21SB
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 7.3. - 22.4.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Schedule will be agreed on the first contact lesson of the course.
Alternative completion methods
Web-based course in Summer 2022
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information for students
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.03.2022 - 31.05.2022
Timing
01.03.2022 - 31.08.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 10
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGAKTIIVILogistiikan aktiivitoteutukset
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin loppukoetta.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Elokuussa loppukoe ja kaksi uusintaa, tarkemmat tenttiajankohdat ilmoitetaan myöhemmin.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information for students
Avoin AMK 10
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 18.03.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 45
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLS21KMMLogistiikan tutkinto-ohjelma (AMK)
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Kontaktitunteja ja/tai konsultaatiota etäyhteydellä pidettävissä webinaareissa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa.
Student workload
konsultaatiotunnit + itsenäinen työskentely (teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information for students
Avoin AMK 10
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 80
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TKN21S1, päivätoteutus (Capacity: 50. Open UAS: 0.)
- TKN21SM, monimuotototeutus (Capacity: 30. Open UAS: 0.)
Groups
-
ZJA21STPMKOAvoin amk, tekniikkan Konetekniikka, monimuoto
-
ZJA21STPPKOAvoin amk, tekniikka, Konetekniikka, päivä
-
TKN21S1Konetekniikka
-
TKN21SMKonetekniikka
Small groups
- TKN21S1,
- TKN21SM
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Course is implemented between 10.1. - 25.3.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Schedule will be agreed on the first contact lesson of the course.
Alternative completion methods
Web-based course in Summer 2022
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information for students
Avoin AMK 5
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Scheduling groups
- Päiväryhmä (Capacity: 40. Open UAS: 0.)
- Monimuoto (Capacity: 40. Open UAS: 0.)
Groups
-
ZJA21STPPENAvoin amk, tekniikka Enegia- ja ympäristötekniikka, päivä
-
ZJA21STPMENAvoin amk, tekniikka, Energia- ja ympäristöteniikka, monimuoto
-
TER21S1Energia- ja ympäristötekniikka (AMK)
-
TER21SMEnergia- ja ympäristötekniikka (AMK)
Small groups
- Päiväryhmä
- Monimuoto
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Opintojakso toteutetaan 10.1.2022 - 27.2.2022
Luennot toteutetaan lähiopetuksena sekä live-streamina verkossa.
Laskuharjoitukset lähiopetuksena päivätoteutuksen opiskelijoille ja verkossa monimuotototeutuksen opiskelijoille.
Teaching methods
Opintojakso koostuu luennoista, ohjatuista laskuharjoituksista, itsenäisestä harjoittelusta ja kokeista.
Exam dates and retake possibilities
Ilmoitetaan opintojakson alussa.
Student workload
3op * 27h/op = 81h
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TSA21SASähkö- ja automaatiotekniikka (AMK)
-
ZJA21STPPSAAvoin amk, tekniikka, Sähkö ja automaatiotekniikka, päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot/laskuharjoitukset 2*2/vko viikoilla 2-8
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Loppukoe kurssin viimeisellä luentokerralla (vko 8). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information for students
Avoin AMK 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
01.01.2022 - 15.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA21SBSähkö- ja automaatiotekniikka (AMK)
-
ZJA21STPPSAAvoin amk, tekniikka, Sähkö ja automaatiotekniikka, päivä
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
luennot/laskuharjoitukset 2*2/vko viikoilla 2-8
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam dates and retake possibilities
Loppukoe kurssin viimeisellä luentokerralla (vko 8). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information for students
Avoin AMK 5 paikkaa
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.10.2021 - 28.02.2022
Timing
01.10.2021 - 31.05.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Online learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
ZJA21STAvoin AMK, tekniikka
-
LOGAKTIIVILogistiikan aktiivitoteutukset
-
ZJA22KTAvoin AMK, tekniikka
Objectives
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Time and location
Tälle toteutukselle ilmoittautuminen alkaa lokakuun alussa ja päättyy helmikuun loppuun mennessä. Lähetä ilmoittautuessasi myös sähköposti osoitteeseen ida.arhosalo@jamk.fi, jotta sinut huomataan heti hyväksyä toteutukselle! Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Loppukokeita järjestetään vähintään kerran kuussa maaliskuusta alkaen (ajankohdat ilmoitetaan työtilassa). Konsultointitunteja etäyhteydellä järjestetään tarpeen mukaan. Niille osallistuminen ei ole välttämätöntä ja ajankohdat ilmoitetaan myöhemmin työtilassa.
Learning materials and recommended literature
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Tarvittaessa konsultaatiota etäyhteydellä pisettävissä webinaareissa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam dates and retake possibilities
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Lähetä ilmoittautuessasi myös sähköposti osoitteeseen ida.arhosalo@jamk.fi, jotta sinut huomataan heti hyväksyä toteutukselle!
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information for students
Avoin AMK 10
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Evaluation criteria, good (3-4)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Evaluation criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Prerequisites
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.