Math2 FunctionsLaajuus (3 cr)
Code: TZLM2300
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.04.2025  30.04.2025
Timing
20.05.2025  31.07.2025
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
 Bachelor's Degree Programme in Construction Management
Teachers
 Kalle Niemi
Groups

UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 20.5.22.8.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in autumn 2025.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  04.05.2025
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
20  30
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Antti Kosonen
Groups

ZJATLS24SMMAvoin amk, Logistiikka, Monimuoto

TLS24SMMLogistiikka  tutkintoohjelma (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 13.1.2025.4.5.2025
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material:
 Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1
 Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Online teaching, independent study. Theory is studied independently using written material and instructional videos. Weekly online guidance provides support for learning and problemsolving exercises.
Active participation in solving exercise tasks is necessary to achieve the learning objectives.
Practical training and working life connections

Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in week 18
First resit in week 21.
Second resit in week 23.
International connections

Alternative completion methods
Information about alternative implementations available on https://opintohaku.jamk.fi/.
Student workload
Average load: 3cr * 27h/cr = 81h.
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
If a student does not show activity within three weeks from the start of the course, their course registration will be rejected.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  27.04.2025
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 Logistics
Teachers
 Antti Kosonen
Scheduling groups
 TLS24SA (Capacity: 35. Open UAS: 0.)
 TLS24SB (Capacity: 35. Open UAS: 0.)
Groups

TLS24S1Logistiikka  tutkintoohjelma (AMK)

ZJATLS24S1Avoin amk, Logistiikka, Päivä
Small groups
 TLS24SA
 TLS24SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 13.1.2025.27.4.2025
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material:
 Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1
 Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Flipped learning: The theory is studied independently using written material and instructional videos before the weekly lesson. During the weekly contact session, the focus is on problemsolving exercises and personal guidance. Attendance is mandatory at the weekly sessions.
Active participation in solving exercise tasks is necessary to achieve the learning objectives.
Practical training and working life connections

Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in week 17
First resit in week 21.
Second resit in week 23.
International connections

Alternative completion methods
Information about alternative implementations available on https://opintohaku.jamk.fi/.
Student workload
Average load: 3cr * 27h/cr = 81h.
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  30.04.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 English
Seats
20  30
Degree programmes
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Kalle Niemi
Groups

ZJATLP24S1Avoin amk, Purchasing and Logistics Engineering, Päivä

TLP25VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies

TLP24S1Bachelor's Degree Programme in Purchasing and Logistics Engineering

TLP24VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 27.1.2025 and 25.4.2025.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
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.
Student workload
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 13.1.2025 and 7.3.2025.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 13.1.2025 and 7.3.2025.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 13.1.2025 and 7.3.2025.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
18.11.2024  09.01.2025
Timing
13.01.2025  21.02.2025
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Implementation remotely during period 3 + Saturday study day
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
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
Content scheduling
The schedule of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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 Math2 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
 Finnish
Seats
20  35
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Pekka Varis
Groups

TSA24SR1Insinööri (AMK), sähkö ja automaatiotekniikka, päivätoteutus

ZJATSA24S1Avoin amk, Sähköja automaatiotekniikka, Päivä
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2025 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
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
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
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.
Opintojaksolla on 80% läsnäolovelvoite. Läsnäoloa seurataan. Poissaoloista sovitaan opettajan kanssa perustelluista syistä (esimerkiksi sairaustapaukset). Läsnäolovelvoitteesta saa vapautuksen myös aiempien opintojen perusteella.
Suositellaan valitsemaan myös opintojakso Mat2 Funktiot tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2024  09.01.2025
Timing
13.01.2025  21.02.2025
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 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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Ville Arvio
Groups

TAR24S1Bachelor's Degree Programme in Automation and Robotics
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented in 3rd period.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
Further information for students
The course includes home assignments, intermediate tests, other assignments, 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2024  09.01.2025
Timing
13.01.2025  07.03.2025
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
 Finnish
Seats
20  35
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Pekka Varis
Groups

TSA24SR2Insinööri (AMK), sähkö ja automaatiotekniikka, päivätoteutus

ZJATSA24S1Avoin amk, Sähköja automaatiotekniikka, Päivä
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2025 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
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
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
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.
Opintojaksolla on 80% läsnäolovelvoite. Läsnäoloa seurataan. Poissaoloista sovitaan opettajan kanssa perustelluista syistä (esimerkiksi sairaustapaukset). Läsnäolovelvoitteesta saa vapautuksen myös aiempien opintojen perusteella.
Suositellaan valitsemaan myös opintojakso Mat2 Funktiot tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
18.11.2024  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  60
Degree programmes
 Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
 Ville Sivil
Scheduling groups
 TRY24SA (Capacity: 35. Open UAS: 0.)
 TRY24SB (Capacity: 35. Open UAS: 0.)
Groups

TRY24S1Rakennus ja yhdyskuntatekniikka (AMK)

ZJATRY24S1Avoin amk, Rakennus ja yhdyskuntatekniikka, Päivä
Small groups
 TRY24SA
 TRY24SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 18.11.2024.9.2.2025
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in the week starting 3.2.2025
1st resit in the week starting 3.3.2025
2nd resit in the week starting 31.3.2025
Alternative completion methods
Any implementation of the TZLM2300 course
Student workload
Approximate time requirement: 3 op * 27 h/op = 81 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  22.08.2024
Timing
18.11.2024  09.02.2025
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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Ville Sivil
Groups

TER24S1Energia ja ympäristötekniikka (AMK)

ZJATER24S1Avoin amk, Energia ja ympäristötekniikka , päivä
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 18.11.2024.9.2.2025
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in the week starting 3.2.2025
1st resit in the week starting 3.3.2025
2nd resit in the week starting 31.3.2025
Alternative completion methods
Any implementation of the TZLM2300 course
Student workload
Approximate time requirement: 3 op * 27 h/op = 81 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
18.11.2024  07.02.2025
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)

TKN24S1Konetekniikka (AMK)

ZJATKN24SMAvoin amk, Konetekniikka, Monimuoto

ZJATKN24S1Avoin amk, Konetekniikka, Päivä
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 18.11.20247.2.2025.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Passing Exam in Examstudio during 7.1.  7.3.
Graded Exam on week 6, reexam on week 8 and last reeaxm on week 10.
Alternative completion methods
Webbased course in Summer 2025
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: automated tests
Regression group assignment
Pass exam
Graded exam
Bonus assignment
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  22.08.2024
Timing
18.11.2024  09.02.2025
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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Ville Sivil
Groups

TER24SMEnergia ja ympäristötekniikka (AMK)

ZJATER24SMAvoin amk, Energia ja ympäristötekniikka, monimuoto
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 18.11.2024.9.2.2025
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Online learning, lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in the week starting 3.2.2025
1st resit in the week starting 3.3.2025
2nd resit in the week starting 31.3.2025
Alternative completion methods
Any implementation of the TZLM2300 course
Student workload
Approximate time requirement: 3 op * 27 h/op = 81 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
26.08.2024  11.10.2024
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  50
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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Pekka Varis
Groups

TSA24KMInsinööri (AMK), sähkö ja automaatiotekniikka,monimuototeutus

ZJATSA24KMAvoin amk, Sähkö ja automaatiotekniikka, Monimuoto
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Opintojakso toteutetaan viikoilla 35  41 (26.8.  11.10.2021)
Learning materials and recommended literature
Opintojakson kirjallinen materiaali sekä videomateriaali julkaistaan opintojakson oppimisympäristössä opintojakson alussa.
Teaching methods
Itsenäinen opiskelu videoluentojen avulla, viikottainen verkkoohjaus.
Exam dates and retake possibilities
Tentin ajankohdat julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Koe tehdään paikan päällä.
Student workload
verkkoohjaukset 12 h
Itsenäiset harjoitukset 32 h
Itsenäinen opiskelu, kokeeseen valmistautuminen sekä koe 35 h
Further information for students
Opintoijakso arvioidaan kurssin lopulla pidettävällä kokeella. Viikottaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
26.08.2024  01.12.2024
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
20  30
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Ville Sivil
Groups

ZJATLS24KMMAvoin amk, Logistiikka, Monimuoto

TLS24KMMLogistiikka  tutkintoohjelma (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 26.8.2024  1.12.2024.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Online learning, lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in the week starting 25.11.2024
1st resit in the week starting 6.1.2025
2nd resit in the week starting 27.1.2025
Alternative completion methods
Any implementation of the TZLM2300 course
Student workload
Approximate time requirement: 3 op * 27 h/op = 81 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
26.08.2024  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  45
Degree programmes
 Bachelor's Degree Programme in Construction Management
Teachers
 Ville Sivil
Groups

TRM24KMMRakennusmestari (AMK), monimuotototeutus

ZJATRM24KMMAvoin amk,Rakennusmestari, Monimuoto
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 19.8.2024  8.12.2024
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Online learning, lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio
Grading exam in the week starting 2.12.2024
1st resit in the week starting 16.1.2025
2nd resit in the week starting 27.1.2025
Alternative completion methods
Any implementation of the TZLM2300 course
Student workload
Approximate time requirement: 3 op * 27 h/op = 81 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2024  22.08.2024
Timing
26.08.2024  01.12.2024
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
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
 Bachelor's Degree Programme in Construction Management
Teachers
 Kalle Niemi
Groups

UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 26.8.  1.12.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in spring or in summer 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.04.2024  30.04.2024
Timing
01.05.2024  31.07.2024
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  40
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 Construction Management
 Bachelor's Degree Programme in Information and Communications Technology
Teachers
 Kalle Niemi
Groups

UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 1.5.23.8.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in autumn 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  14.01.2024
Timing
11.03.2024  26.04.2024
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

TLP23VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies

TLP24VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies

ZJATLP23S1Avoin amk, Purchasing and Logistics Engineering, Päivä

TLP23S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (a 90min) per week during weeks 1116. One rehearsal lesson and exam in week 17.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.04.2024  30.04.2024
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 Construction Management
 Bachelor's Degree Programme in Information and Communications Technology
Teachers
 Kalle Niemi
Groups

UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Summer studies/ITinstitute students (20).
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in summer 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 8.1. and 23.2.24.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  15.03.2024
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  40
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Kalle Niemi
Groups

ZJATLS23SMMAvoin amk, Logistiikka, Monimuoto

TLS23SMMLogistiikka  tutkintoohjelma (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 8.1.2024  15.3.2024
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Online/recorded lectures, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisellä tunnilla.
Alternative completion methods
Webbased course in Summer 2024
Student workload
Lectures 7 x 2 h = 14 h
Guided exercises 6 x 1 h = 12 h
Independent study of theory 14 h
Exercises at home 21 h
Homework 12 h ( 6 pcs) + Tests 4 h (2 pcs)
Preparation for exams 6 h
Exams 4 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  15.03.2024
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 Logistics
Teachers
 Kalle Niemi
Scheduling groups
 TLS23SA (Capacity: 35. Open UAS: 0.)
 TLS23SB (Capacity: 35. Open UAS: 0.)
Groups

ZJATLS23S1Avoin amk, Logistiikka, Päivä

TLS23S1Logistiikka  tutkintoohjelma (AMK)
Small groups
 TLS23SA
 TLS23SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 8.1.2024  15.3.2024
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisellä tunnilla.
Alternative completion methods
Webbased course in Summer 2024
Student workload
Lectures 7 x 2 h = 14 h
Guided exercises 6 x 2 h = 12 h
Independent study of theory 8 h
Exercises at home 21 h
Homework 12 h ( 6 pcs) + Tests 4 h (2 pcs)
Preparation for exams 6 h
Exams 4 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 8.1. and 23.2.24
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 8.1. and 23.2.24
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
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
 Ville Arvio
Groups

TTV23S5Tieto ja viestintätekniikka (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 8.1. and 23.2.24
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  23.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
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
 Ville Arvio
Groups

TTV23SMTieto ja viestintätekniikka (AMK)

ZJATTV23SMAvoin amk, Tieto ja viestintätekniikka, Monimuoto
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 8.1. and 23.2.24
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
08.01.2024  25.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
 Finnish
Seats
0  60
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Pekka Varis
Groups

TSA23SR1Sähkö ja automaatiotekniikka (AMK)

TSA23SR2Sähkö ja automaatiotekniikka (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2024 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023  04.01.2024
Timing
01.01.2024  23.02.2024
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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Ida Arhosalo
Groups

TAR23S1Bachelor's Degree Programme in Automation and Robotics
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons(90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
23.08.2023  01.11.2024
Timing
20.11.2023  09.02.2024
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
 Antti Kosonen
Scheduling groups
 TRY23SA (Capacity: 30. Open UAS: 0.)
 TRY23SB (Capacity: 30. Open UAS: 0.)
Groups

TRY23S1Rakennus ja yhdyskuntatekniikka (AMK)

ZJATRY23S1Avoin amk, Rakennus ja yhdyskuntatekniikka, Päivä
Small groups
 TRY23SA
 TRY23SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 20.11.2023.11.2.2024
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Test to pass the course in Exam studio January 14 to March 7.
Grading exam in week 6, 1st resit in week 10 and 2nd resit on week 12.
Alternative completion methods
Webbased course in Summer 2024
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  24.08.2023
Timing
20.11.2023  31.01.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 Finnish
Seats
0  92
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 20.11.2023.31.1.2024
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examstudiossa aikavälillä 14.1.  7.3.
Arvosanakoe viikolla 5, sen uusintakoe 1 viikolla 8 ja uusintakoe 2 viikolla 11.
Alternative completion methods
Webbased course in Summer 2024
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  24.08.2023
Timing
16.10.2023  04.02.2024
Number of ECTS credits allocated
3 op
Virtual portion
1.5 op
Mode of delivery
50 % Facetoface, 50 % Online learning
Unit
School of Technology
Teaching languages
 Finnish
Seats
0  70
Degree programmes
 Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
 Antti Kosonen
Scheduling groups
 TER23S1 (Capacity: 45. Open UAS: 0.)
 TER23SM (Capacity: 45. Open UAS: 0.)
Groups

ZJATER23S1Avoin amk, Energia ja ympäristötekniikka , päivä

TER23S1Energia ja ympäristötekniikka (AMK)

TER23SMEnergia ja ympäristötekniikka (AMK)

ZJATER23SMAvoin amk, Energia ja ympäristötekniikka , monimuoto
Small groups
 Scheduling group 1
 Scheduling group 2
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 13.11.2023  4.2.2024.
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.
 Rantakaulio, A. & Lehtola, P. 2013. Tekninen matematiikka: 2. 1. uus. p. Tampere: Tammertekniikka.
 Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.
Teaching methods
Lectures, guided exercises, independent work, exams.
Lectures will also be streamed online.
Guided exercises will be held at campus or online depending on the implementation of your degree programme.
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 5 (2024), depending on your degree programme.
The exam that determines the grade will be held for everyone during week 5 starting on January 29, 2024.
The first resit exam will be held
 on February 21, 2024 for the traditionalmode course
 on February 22, 2024 for the flexiblemode course
The second resit exam will be held
 on March 20, 2024 for traditionalmode course
 on March 21, 2024 for the flexiblemode course
International connections

Alternative completion methods
Facetoface, hybrid and online implementations are available in autumn and in spring. It is also possible to attend the course online during summer 2024.
Student workload
Calculatory workload: 3cr * 27h/cr = 81h
Weekly use of time:
Lectures 2 * 45 min
Exercises 2 * 45 min
Additionally:
 Exams approximately 4 h
 Independent work approximately 55  60 h
Content scheduling
More detailed schedule will be announced at the beginning of the course, but the topics will be covered roughly in the following order:
 Revision and Supplementation of Functions
 Exponential Functions
 Logarithms
 Trigonometric Functions
 Trigonometric Functions
 Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and tests / exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
 Bachelor's Degree Programme in Construction Management
Teachers
 Kalle Niemi
Groups

UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 28.8.  17.12.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in spring or in summer 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  24.08.2023
Timing
21.08.2023  03.12.2023
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  40
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Kalle Niemi
Groups

TLS23KMMLogistiikka  tutkintoohjelma (AMK)

ZJATLS23KMMAvoin amk, AMKpolut, Logistiikka, Monimuoto
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course will be carried 21.8.2023  12.11.2023.
Learning materials and recommended literature
Written material and video material on Moodle.
Teaching methods
Onlinelessons, contact teaching, independent work.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisessä tapaamisessa.
Alternative completion methods
Independently conducted online course during autumn or spring. Facetoface implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  24.08.2023
Timing
21.08.2023  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  30
Degree programmes
 Bachelor's Degree Programme in Construction Management
Teachers
 Kalle Niemi
Teacher in charge
Kalle Niemi
Groups

ZJATRM23KMMAvoin amk, AMKpolut, Rakennusmestari, Monimuoto

TRM23KMMRakennusmestari (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course will be carried 21.8.2023  12.11.2023.
Learning materials and recommended literature
Written material and video material on Moodle.
Teaching methods
Onlinelessons, contact teaching, independent work.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisessä tapaamisessa.
Alternative completion methods
Independently conducted online course during autumn or spring. Facetoface implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023  24.08.2023
Timing
01.08.2023  15.10.2023
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
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 Construction Management
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Pekka Varis
Groups

TSA23KMInsinööri (AMK), sähkö ja automaatiotekniikka,monimuototeutus
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Opintojakso toteutetaan viikoilla 35  41 (28.8.  13.10.2021)
Learning materials and recommended literature
Opintojakson kirjallinen materiaali sekä videomateriaali julkaistaan opintojakson oppimisympäristössä opintojakson alussa.
Teaching methods
Itsenäinen opiskelu videoluentojen avulla, viikottainen verkkoohjaus
Exam dates and retake possibilities
Kokeen ajankohdat julkaistaan oppimisympäristössä opintojakson alussa. Kokeen voi tehdä paikan päällä tai etänä.
Student workload
verkkoohjaukset 9 h
Itsenäiset harjoitukset 32 h
Itsenäinen opiskelu, kokeeseen valmistautuminen sekä koe 40 h
Further information for students
Opintoijakso arvioidaan kurssin lopulla pidettävällä kokeella. Viikottaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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  5
Degree programmes
 Bachelor's Degree Programme in Logistics
 Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

LOGRAKVERKKOLogistiikan ja rakentamisen verkkoopetus
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 01.05.2023  31.08.2023.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
Exam dates will be published in Moodle at the beginning of the implementation.
Alternative completion methods
Facetoface, hybrid or online implementation in autumn 2023 or spring 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
07.03.2023  30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 Finnish
Seats
0  60
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Kalle Niemi
Scheduling groups
 TLS22SA (Capacity: 35. Open UAS: 0.)
 TLS22SB (Capacity: 35. Open UAS: 0.)
Groups

TLS22S1Logistiikka  tutkintoohjelma (AMK)

ZJATLS22S1Avoin amk, Logistiikka, Päivä
Small groups
 TLS22SA
 TLS22SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 30.3.2023  30.4.2023
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisellä tunnilla.
Alternative completion methods
Webbased course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 9.1.2023 and 24.2.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated total workload is 81 hours, which is divided by approximately 20% to contact teaching and 80% for independent work.
Content scheduling
The course timetable is agreed on at the beginning of the course and then published in the elearning environment.
Further information for students
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu hyväksytysti.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2023 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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  140
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 9.1.2023 and 24.2.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated total workload is 81 hours, which is divided by approximately 20% to contact teaching and 80% for independent work.
Further information for students
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen osallistumista. Jotta läpäisytestiin ja arvosanakokeeseen voi osallistua, täytyy opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) olla hyväksytysti tehty.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2023 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Facetoface, 33 % Online learning
Unit
School of Technology
Campus
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 9.1. and 24.2.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 9.1.2023 and 24.2.2023.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The course timetable is agreed on at the beginning of the course and then published in the elearning environment.
Further information for students
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen osallistumista. Jotta läpäisytestiin ja arvosanakokeeseen voi osallistua, täytyy opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) olla hyväksytysti tehty.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 9.1. and 24.2.
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  19.05.2023
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

TLP23VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies

TLP22S1Bachelor's Degree Programme in Purchasing and Logistics Engineering

ZJATLP22S1Avoin amk, Purchasing and Logistics Engineering, Päivä

TLP22VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
One lesson(90min) per week during weeks 28 and 1116.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

LOGRAKVERKKOLogistiikan ja rakentamisen verkkoopetus
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 9.1.2023  19.5.2023.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
Possible dates for exam / resit:
 18.1.2023
 8.2.2023
 22.3.2023
 12.4.2023
 17.5.2023
 31.5.2023
Alternative completion methods
Facetoface or hybrid implementation in spring. Online course in spring or in summer 2023.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 28.11.2022  17.2.2023
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examstudiossa aikavälillä 23.1.  10.3.
Arvosanakoe viikolla 7, sen uusintakoe 1 viikolla 10 ja uusintakoe 2 viikolla 13.
Alternative completion methods
Webbased course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  19.05.2023
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  50
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Kalle Niemi
Teacher in charge
Kalle Niemi
Groups

ZJATLS22SMMAvoin amk, Logistiikka, Monimuoto

TLS22SMMLogistiikka  tutkintoohjelma (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course will be carried out 9.1.2023  26.4.2023.
Learning materials and recommended literature
Written material and video material prepared by teacher.
Teaching methods
Onlinelessons, contact teaching, independent work.
Exam dates and retake possibilities
Will be announced at the first meeting of the course.
Alternative completion methods
Independently conducted online course during autumn or spring. Facetoface implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  26.02.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 Finnish
Seats
0  65
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups

ZJATSA22S1Avoin amk, Sähkö ja automaatiotekniikka, Päivä

TSA22SR1Sähkö ja automaatiotekniikka (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 9.1.2023  24.2.2023
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Ilmoitetaan ensimmäisellä tunnilla.
Alternative completion methods
Webbased course in Summer 2023
Student workload
Lectures, quided exercises and exam 30 h
Independent work and automatic tests 51 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022  05.01.2023
Timing
09.01.2023  26.02.2023
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
 Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups

TSA22SR2Sähkö ja automaatiotekniikka (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
21.11.2022  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
 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
 Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups

TAR22S1Bachelor's Degree Programme in Automation and Robotics
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022  25.08.2022
Timing
31.10.2022  18.12.2022
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  60
Degree programmes
 Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
 Antti Kosonen
Scheduling groups
 Päiväryhmä TER22S1 (Capacity: 50. Open UAS: 0.)
 Monimuotoryhmä TER22SM (Capacity: 50. Open UAS: 0.)
Groups

TER22S1Energia ja ympäristötekniikka (AMK)

TER22SMEnergia ja ympäristötekniikka (AMK)

ZJATER22S1Avoin amk, Energia ja ympäristötekniikka

ZJATER22SMAvoin amk, Energia ja ympäristötekniikka , monimuoto
Small groups
 Pienryhmä 1
 Pienryhmä 2
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 31.10.2022  18.12.2022.
Lectures will also 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.
 Rantakaulio, A. & Lehtola, P. 2013. Tekninen matematiikka: 2. 1. uus. p. 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 50, depending on the implementation of your degree programme.
A gradedetermining exam will take place during week 50.
First resit 18.1.2023
Second resit 8.2.2023
Alternative completion methods
Facetoface, hybrid and online implementations are available in autumn and in spring. 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. Revision and Supplementation of Functions
2. Exponential Functions
3. Logarithms
4. Trigonometric Functions
5. Trigonometric Functions
6. Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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  20
Degree programmes
 Bachelor's Degree Programme in Logistics
 Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

LOGRAKVERKKOLogistiikan ja rakentamisen verkkoopetus
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented 29.8.  18.12.
Learning materials and recommended literature
Videos and written material in elearning environment Moodle.
Recommended literature (in Finnish):
 Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
 Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam dates and retake possibilities
Possible dates for exam / resit:
 9.11.2022
 30.11.2022
 14.12.2022
 18.1.2023
 8.2.2023
Alternative completion methods
Facetoface or hybrid implementation in autumn or in spring. Online course in spring or in summer 2023.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
 32 h of studying the material
 45 h of exercises
 4 h for exams.
Content scheduling
A detailed schedule will be available in the elearning environment when the course starts.
Further information for students
Summative assessment is based on a twopart final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022  25.08.2022
Timing
29.08.2022  13.11.2022
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  40
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

ZJA22KTPMLAvoin AMK, tekniikka, Logistiikka, monimuoto

ZJA21STPMLAvoin amk, tekniikka, Logistiikka monimuoto

TLS22KMMLogistiikan tutkintoohjelma (AMK)
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course will be carried out 29.8.2022  13.11.2022.
Learning materials and recommended literature
Written material and video material prepared by teacher.
Teaching methods
Onlinelessons, contact teaching, independent work.
Exam dates and retake possibilities
Final exam in two parts during week 45.
Alternative completion methods
Independently conducted online course during autumn or spring. Facetoface implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information for students
Assessment is based on twopart final exam and exercises.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022  25.08.2022
Timing
15.08.2022  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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 28.11.2022.11.2.2023
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures facetoface, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam dates and retake possibilities
Läpäisykoe Examstudiossa aikavälillä 16.1.  10.3.
Arvosanakoe viikolla 6, sen uusintakoe 1 viikolla 10 ja uusintakoe 2 viikolla 13.
Alternative completion methods
Webbased course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2022 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Kevätlukukauden 2022 ensimmäinen puolisko.
Learning materials and recommended literature
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Facetoface, 33 % Online learning
Unit
School of Technology
Campus
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 10.1.2022 and 25.2.2022
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
Further information for students
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit (3 kpl). Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 10.1.2022 and 25.2.2022
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately fifty  fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
Further information for students
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit (3 kpl). Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Facetoface, 66 % Online learning
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
 Sirpa Alestalo
 Kalle Niemi
Groups

TTV21SMTieto ja viestintätekniikka (AMK)

ZJA21STPMTVAvoin amk, tekniikka, Tieto ja viestintätekniikka, verkko
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
The course is implemented between 10.1.2022 and 11.3.2022
Learning materials and recommended literature
Course material consists of written material and video material available in the elearning environment.
Recommended literature:
 Alestalo, Lehtola, Nieminen, Rantakaulio  Tekninen matematiikka 1 (in Finnish)
 Henttonen, Peltomäki, Uusitalo  Tekniikan matematiikka 1 (in Finnish)
 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately twenty eighty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the elearning environment.
Further information for students
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvän läpäisytestin. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Two lessons (90min) per week during weeks 28.
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.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  29.04.2022
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 Logistics
Teachers
 Ville Sivil
Teacher in charge
Antti Kosonen
Scheduling groups
 TLS21SA (Capacity: 40. Open UAS: 0.)
 TLS21SB (Capacity: 40. Open UAS: 0.)
Groups

ZJA21STPPLOAvoin amk, tekniikka, Logistiikka päivä

TLS21S1Logistiikan tutkintoohjelma (AMK)
Small groups
 TLS21SA
 TLS21SB
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 10.1.2022  27.2.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1
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.
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 41 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  29.03.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 Finnish
Seats
0  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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Course is implemented between 10.1.25.2.2022.
Learning materials and recommended literature
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo  Lehtola  Nieminen  Rantakaulio: Tekninen matematiikka 1 and in Lehtola  Rantakaulio: Tekninen matematiikka 2
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, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information for students
Avoin AMK 5
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  23.01.2022
Timing
10.01.2022  25.02.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
Campus
Main Campus
Teaching languages
 English
Seats
0  35
Degree programmes
 Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
 Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups

TLP21S1Bachelor's Degree Programme in Purchasing and Logistics Engineering

TLP21VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies

ZJA21STPPLPAvoina amk, tekniikka, Logistics and purchasing, päivä

TLP22VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihtoopiskelu/Exchange studies
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
One lesson(90min) per week during weeks 216.
Learning materials and recommended literature
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam dates and retake possibilities
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021  09.01.2022
Timing
10.01.2022  20.05.2022
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  20
Degree programmes
 Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

TSA22KMInsinööri (AMK), sähkö ja automaatiotekniikka,monimuototeutus
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Opintojakso toteutetaan 7.3.2022  7.5.2022.
Learning materials and recommended literature
Kurssilla saat käyttöösi opintojaksoa varten laaditut oppimateriaalit (kirjallinen ja videomateriaali)
Teaching methods
Verkkoopetus, kontaktiopetus, itsenäinen työsentely.
Exam dates and retake possibilities
Läpäisykoe pe 6.5.
Arvosanakoe la 7.5.
Uusintojen ajankohdat sovitaan aloitustapaamisessa.
Alternative completion methods
Verkkototeutus kesällä 2022.
Student workload
3op * 27h/op = 81h
Further information for students
Osaamista arvioidaan kaksiosaisella loppukokeella.
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Timing
03.01.2022  31.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Facetoface
Unit
School of Technology
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
 Antti Kosonen
Groups

ZJA21KTPMLAvoin AMK, tekniikka, AMKpolut, logistiikka
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Opintojakso toteutetaan 7.3.2022  7.5.2022.
Learning materials and recommended literature
Kurssilla saat käyttöösi opintojaksoa varten laaditut oppimateriaalit (kirjallinen ja videomateriaali)
Teaching methods
Verkkoopetus, itsenäinen työsentely.
Alternative completion methods
Verkkototeutus kesällä 2022.
Student workload
3op * 27h/op = 81h
Further information for students
AVOIN AMK
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
02.08.2021  31.05.2022
Timing
30.08.2021  30.08.2022
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  15
Degree programmes
 Bachelor's Degree Programme in Logistics
Teachers
 Antti Kosonen
Teacher in charge
Antti Kosonen
Groups

ZJK22KTKorkeakoulujen välinen yhteistyö, TEKN

ZJA21STAvoin AMK, tekniikka

LOGAKTIIVILogistiikan aktiivitoteutukset

ZJA22KTAvoin AMK, tekniikka
Objectives
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
 The notion of a function and the notation related to functions
 Logarithmic functions and equations
 Exponential functions and equations
 Trigonometric functions: the sine curve
 The use of functions in modelling
 Piecewise defined functions
 Combined functions
 Inverse functions
 Limit of a function
Time and location
Elearning course. Implementation starts 30.8.
Learning materials and recommended literature
Written material and video material.
Teaching methods
The course will be conducted independently in an elearning environment. The course material consists of written and and video material, exercises and a final exam.
Exam dates and retake possibilities
Schedule will be announced in the elearning environment
Student workload
3 cr * 27 h/cr = 81 h.
Further information for students
Avoin AMK syksy 5
Avoin AMK polku kevät 15
Avoin AMK kevät 5
Avoin AMK kesä 10
CampusOnline 20
Evaluation scale
05
Evaluation criteria, satisfactory (12)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Evaluation criteria, good (34)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary functionrelated equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve functionrelated equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Evaluation criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve functionrelated equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Prerequisites
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.