Math2 Functions (3 cr)

Evaluation scale

0-5

Content scheduling

Will be agreed on the first contact lesson of the course.

Objective

Course purpose

During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.

Course competences

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

Location and time

Course is implemented between 17.11.2025-6.2.2026.

Materials

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

Lessons, recordings, guided exercises (contact in web), booklet tasks, independent work, automatic tests, exam.

Exam schedules

Passing Exam in Exam-studio during 12.1. - 19.2.
Graded Exam on 6.2., re-exam on 12.2. and last re-eaxm on 19.2.

Completion alternatives

Web-based course in Summer 20256

Student workload

Lectures, recordings, quided exercises and exam 40 h
Independent work and automatic tests 40 h

Assessment criteria, satisfactory (1)

Grade 1

You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.

Grade 2

You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.

Assessment criteria, good (3)

Grade 3

You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary 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.

Assessment criteria, excellent (5)

Grade 5

You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.

Qualifications

You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.

Further information

Continuous feedback: automated tests
Regression group assignment
Pass exam
Graded exam
Bonus assignment