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
EURACE: 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
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
 Finnish
Seats
20  30
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, Sähköja 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
EURACE: 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
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 1117
Läpäisykoe Examstudiossa
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 Examstudiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
 Finnish
Seats
20  30
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Ida Arhosalo
Groups

TSA24SR2Insinööri (AMK), sähkö ja automaatiotekniikka, päivätoteutus

ZJATSA24S1Avoin amk, Sähköja 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
EURACE: 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
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 1117
Läpäisykoe Examstudiossa
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 Examstudiossa
Arvosanakoe viikolla 17, uusintojen ajankohdat kerrotaan toteutuksen työtilassa ja ensimmäisellä luennolla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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

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
EURACE: 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
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 1016.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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

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
EURACE: 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
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 1016.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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

TTV24SMTieto ja viestintätekniikka (AMK)

ZJATTV24SMAvoin 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
EURACE: 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
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
Implementation remotely during period 4 + Saturday study day
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Lehtola, Rantakaulio  Tekninen matematiikka 2 (in Finnish)
Teaching methods
Weekly contact teaching (2+2 h/week), weekly exercises and homework exercises, project work, independent studying from theory material, exams.
Exam dates and retake possibilities
Schedule of the exams and two resits will be given in the beginning of the course.
The course ends with a resit2. After this, coursework returns are no longer accepted and the incomplete course must be retaken in its entirety at the next course implementation.
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
Alternative completion methods
Possibility to take an exam at the beginning of the course on the Exam Studio platform or on other means of organising the exam. In addition, coursework must be returned to Moodle.
Student workload
The estimated workload of the course is 3 credits * 27 h/cr = 81 h.
Contact teaching and councelling approx. 30 h
Weekly exercises and tests 6 x 6 h = 36 h
Independent study of material, preparation for exams and project work 12 h
Final exams 3 h
Further information for students
Assessment methods:
The course includes compulsory assignments, homework and midterm tests. Assessment will be by means of an endofcourse pass/fail exam and with a grade exam. A pass mark of grade 1 is awarded on completion of the compulsory elements of the course and succeeding in the pass/fail exam. A higher grade requires participation in an grade exam.
It is also recommended to choose the course Math3 Support if you have no background in upper secondary school long mathematics or if you need to build up your calculation routine.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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  tutkintoohjelma (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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla. Läpäisykoe on Examstudiossa.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
 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
EURACE: 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
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 PDFmateriaalia.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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 Examstudiossa. Arvosanakokeita järjestetään loppukeväästä. Arvosanakokeet mahdollisesti Examstudiossa 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 25: Pakollisia harjoitustehtäviä, läpäisykoe hyväksytysti, lisäksi arvosanat 25 perustuvat arvosanakokeen pisteisiin.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
 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
EURACE: 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
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 PDFmateriaalia.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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  tutkintoohjelma (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
EURACE: 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
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 3750
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla. Läpäisykoe Examstudiossa itselle sopivaan ajankohtaan ennen arvosanakoetta.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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) vaihtoopiskelu/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
EURACE: 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
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 facetoface, 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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  tutkintoohjelma (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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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/ITinstituutin 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 Examstudiossa Examstudion aukioloaikojen puitteissa.)
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1016.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1015, 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 facetoface 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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  tutkintoohjelma (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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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  tutkintoohjelma (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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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  tutkintoohjelma (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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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) vaihtoopiskelu/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
EURACE: 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
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 facetoface, 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 verkkoopetus
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
EURACE: 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
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 3235.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1016.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 elearning 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 elearning 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1016
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 uusintaajankohdat 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 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1015, 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 eexam studio or as a more traditional supervised exam during week 8, depending on the implementation of your degree programme.
The gradedetermining exam will take place during week 8.
First resit 22.3.2023
Second resit 12.4.2023
Alternative completion methods
Facetoface 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 twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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 verkkoopetus
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
EURACE: 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
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 817. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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 tutkintoohjelma (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
EURACE: 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
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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 tutkintoohjelma (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
EURACE: 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
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 3541
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 uusintaajankohdat 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 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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 verkkoopetus
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
EURACE: 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
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 4149. Viikon 41 kokeet on Rajakadulla luokassa. Viikoilla 4349 järjestetään 3 etävalvottua koetta.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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) vaihtoopiskelu/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
EURACE: 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
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 3540, 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 facetoface 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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, Tietoja 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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 verkkooppimisympäristössä.
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 verkkooppimisympäristössä.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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, Tietoja 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
EURACE: 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
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 verkkooppimisympäristössä.
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 verkkooppimisympäristössä.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 opintooppaassa. 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 verkkoopinnot 20 paikkaa
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 1016.
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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 tutkintoohjelma (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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 facetoface, 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
Webbased 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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 % Facetoface, 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
EURACE: 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
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 livestreamina 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
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 28
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Further information for students
Avoin AMK 5 paikkaa
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
Facetoface
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
EURACE: 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
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 28
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 uusintaajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 2530h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 5060h
Further information for students
Avoin AMK 5 paikkaa
Evaluation scale
05
Evaluation criteria, satisfactory (12)
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 (34)
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
EURACE: 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
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
05
Evaluation criteria, satisfactory (12)
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 (34)
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.