Course Objectives

Recognise and understand the mathematical concepts which are necessary for further studies at universities and scientific university colleges.

The students will become familiar with the fundamental concepts and solution methods associated with:

• Laplace transforms, especially related to solving ordinary and partial differential equations
• Fourier series, Fourier integrals and Fourier transforms, especially related to solving partial differential equations

In connection with calculations and graphics, the students should be able to use the computer program Maple.

Course Description

Laplace transforms: Transforms and inverse transforms. Transformation theorems. Solution of ordinary differential equations.

Fourier series: Orthogonality. Fourier series representation of periodic functions. Fourier sine and Fourier cosine series. Half periodic extentions.
Fourier transforms and integrals: Fourier integrals and Fourier transforms in general. Even and odd functions.
Partial differential equations: Classification. D'Alembert's solution. Sepatation of variables. Solution methods using Fourier series, Fourier transforms and Laplace transforms.

Learning Methods

Lectures and exercises will, in part, require the use of Maple on laptop computers as a working tool.

Assessment Methods

Written mid-term examination and final written examination.

For all examinations, all printed and written aids as well as laptop computers and calculators are permitted.

The final grade for the course is calculated as follows:

Mid-term examination 30%

Final examination: 70%

The final examination must receive a passing mark.

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