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

The course is implemented in 3rd period.

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.

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, other assignments, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.

Evaluation scale

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.