Study Guide

Objective

After completing the course the student:
- operate with mathematical expressions related to technology
- to formulate mathematical model
- understand the concept of a function and recognizes the characteristic properties of different functions
- solve equations involving functions and apply them in practical problems
- use derivatives to analyse graphs
- use differentials to approximate changes and errors
- use matrices and determinants (e.g. for solving linear simultaneous equations),
- use dot and cross products in applications
- give the answer in an expected form

Content

Topics covered in course are (in the order shown):
* functions and graphs
* Pythagoras’ theorem and trigonometric functions
* line and slope
* exponential and logarithmic functions
* function composition
* continuity and limit of a function
* definition of the derivative
* derivatives of basic functions
* derivative rules
* derivative of the composition of functions (chain rule)
* product rule and quotient rule
* tangent and differential
* critical points and extreme values
* finding extreme values by examination of critical points
* functions of several variables
* partial derivatives
* differentials and error estimates
* total differential

Teaching methods

Course consist of lectures and independent calculation exercises, and also of guided calculation exercises as time permitting. There are two long classroom sessions, consisting of lectures and guided calculation exercises. Other lectures are one-hour Teams sessions.

Student workload

Course is worth 5 credits. This means that the estimated workload is 5 * 27 h = 135 h.

Evaluation scale

H-5