Curricula

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 verkko-ohjaus.

Exam dates and retake possibilities

Tentin ajankohdat julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Koe tehdään paikan päällä.

Student workload

verkko-ohjaukset 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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

Face-to-face 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 e-learning environment when the course starts.

Further information for students

Summative assessment is based on a two-part final exam.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 11-16. 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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/IT-institute students (20).

Learning materials and recommended literature

Videos and written material in e-learning 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

Face-to-face 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 e-learning environment when the course starts.

Further information for students

Summative assessment is based on a two-part final exam.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2023

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 2-8.

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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Ilmoitetaan ensimmäisellä tunnilla.

Alternative completion methods

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2024

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2024

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2024

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2024

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 2-8.

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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, 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

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 14.1. - 7.3.
Arvosanakoe viikolla 5, sen uusintakoe 1 viikolla 8 ja uusintakoe 2 viikolla 11.

Alternative completion methods

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-exam 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 traditional-mode course
- on February 22, 2024 for the flexible-mode course

The second resit exam will be held
- on March 20, 2024 for traditional-mode course
- on March 21, 2024 for the flexible-mode course

International connections

-

Alternative completion methods

Face-to-face, 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 two-part final exam and tests / exercises.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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

Face-to-face 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 e-learning environment when the course starts.

Further information for students

Summative assessment is based on a two-part final exam.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

Online-lessons, contact teaching, independent work.

Exam dates and retake possibilities

Ilmoitetaan ensimmäisessä tapaamisessa.

Alternative completion methods

Independently conducted online course during autumn or spring. Face-to-face 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 two-part final exam and exercises.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

Online-lessons, contact teaching, independent work.

Exam dates and retake possibilities

Ilmoitetaan ensimmäisessä tapaamisessa.

Alternative completion methods

Independently conducted online course during autumn or spring. Face-to-face 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 two-part final exam and exercises.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 verkko-ohjaus

Exam dates and retake possibilities

Kokeen ajankohdat julkaistaan oppimisympäristössä opintojakson alussa. Kokeen voi tehdä paikan päällä tai etänä.

Student workload

verkko-ohjaukset 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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

Face-to-face, 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 e-learning environment when the course starts.

Further information for students

Summative assessment is based on a two-part final exam in which you can participate at Rajakatu campus or online.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Ilmoitetaan ensimmäisellä tunnilla.

Alternative completion methods

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning 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 e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 2-8.

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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2023

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning 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 e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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 e-learning environment.

Alternative completion methods

Online course in Summer 2023

Student workload

The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.

Content scheduling

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 2-8 and 11-16.

Learning materials and recommended literature

Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.

Teaching methods

Weekly 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 e-learning 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

Face-to-face 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 e-learning environment when the course starts.

Further information for students

Summative assessment is based on a two-part final exam in which you can participate at Rajakatu campus or online.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 23.1. - 10.3.
Arvosanakoe viikolla 7, sen uusintakoe 1 viikolla 10 ja uusintakoe 2 viikolla 13.

Alternative completion methods

Web-based 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

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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

Online-lessons, 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. Face-to-face 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 two-part final exam and exercises.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

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 (3-4)

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 function-related 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 function-related 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 function-related 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.

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

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

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

In this course, you will expand your range of mathematical tools by learning about the concept of functions and the use of different types of functions to model engineering phenomena. You will understand the concept of a function, identify different types of functions and their properties. You will learn how to use equations to consider functions and how to use different types of functions to model simple engineering phenomena. This course will give you a strong basis for applying mathematical methods in engineering.

- 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 face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Ilmoitetaan ensimmäisellä tunnilla.

Alternative completion methods

Web-based 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