Math2 Functions (3 cr)

Evaluation scale

0-5

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
- Composite Functions and Inverse Functions
- Limits and Continuity of Functions

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

The course is implemented 10.11.2025 - 15.2.2026.

Materials

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 (streamed and available online afterwards), guided exercises online, independent work, exams.

Employer connections

-

Exam schedules

The course exam sessions will take place during the week starting on 9 February 2026.

The first retake session will be during the week starting on 2 March 2026.

The second retake session will be during the week starting on 23 March 2026.

The course pass/fail exam can also be completed in the Exam Studio.

International connections

-

Completion alternatives

Face-to-face, hybrid and online implementations are available in autumn and in spring.

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

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

Assessment is based on two-part final exam and tests / exercises.