Course Objectives

The students will:

• become familiar with the definitions and concepts of Laplace transformations.
• be able to use Laplace transformations as a method of solving ordinary differential equations and systems of such equations.
• know the definitions and concepts related to Fourier series.
• be able to develop functions in Fourier series.
• be conversant with definitions and concepts related to multi-variable functions.
• be able to use the theory of multi-variable functions in connection with, among other uses, error calculations and extremalisation.
• be able to use the computer program Maple for all types of calculations and graphics in connection with exercises.

Course Description

Laplace transformations: Transformation equations, convolution, transformation of periodic functions. Impulses. Dirac’s delta function:

Fourier series: Orthogonality, periodic functions, Fourier sinus series and Fourier cosine series. Half-periodic expansions.

Functions of several variables: Partial derivatives. Classification of critical points. Differentials and finite differences. Error calculations.

Learning Methods

Lectures and exercises.

Assessment Methods

• Maple-project in groups (with a maximum of 4 students per group) (30%) .
• Individual written final examination (70%).

The final written examination must receive a passing grade.

During examinations, all printed and written aids, as well as laptops and calculators will be permitted.

Minor adjustments may occur during the academic year, subject to the decision of the Dean