Entry requirements

Linear Algebra II, Single Variable Calculus or Series and Ordinary Differential Equations

Learning outcomes

In order to pass the course the student should be able to:

• give an account of the definitions and properties of the Laplace transform, the z-transform and the Fourier transform;
• use transformation rules to compute transforms, and to use tables to compute inverse transforms;
• compute Fourier coefficients and know some criterion for pointwise convergence of a Fourier series;
• give an account of the concept of a complete ON-system and be familiar with and know how to apply the theorems of Parseval and Plancherel;
• formulate important results and theorems covered by the course;
• use transforms as a technique for solving differential equations and difference equations;
• use transform methods in some area of applications that is characteristic for the education program of the student and to demonstrate this ability by accomplishing a minor project.

Content

The Laplace transform, the z-transform, Fourier series, the Fourier transform. Applications to ordinary and partial differential equations. A project in a selected area of applications, e.g. circuit electronics, spectral analysis, the discrete Fourier transform.

Instruction

Lectures and problem solving sessions. Laboratory work may occur as part of the project.

Assessment

Written examination (4 credit points) at the end of the course. Written project report (1 credit point). Moreover, compulsory assignments may be given during the course.