# Transform Methods

5 credits

Syllabus, Bachelor's level, 1MA034

Code
1MA034
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 9 November 2021
Responsible department
Department of Mathematics

## Entry requirements

5 credits mathematics. Participation in Single Variable Calculus and one of Linear Algebra and Geometry I, Algebra and Geometry or Algebra and Vector Geometry.

## Learning outcomes

On completion of 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 standard rules for transforms to compute transforms of elementary functions; and use tables to compute inverse transforms;
• compute Fourier coefficients of periodic functions and apply some criterion for pointwise convergence of a Fourier series;
• 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 completing a minor project.

## Content

Fundamentals of Fourier series, Fourier-, Laplace- and z-transforms: linearity, shifting, damping, scaling, behaviour with respect to differentiation and integration. Convolution. Initial and Final Value Theorems. Applications to differential and difference equations.

Discrete and continuous linear time-invariant systems: causality and time invariance. Criteria for stability.

Partial differential equations: separation of variables.

Project with the purpose of deepening the understanding of the properties of transforms and their use in relevant areas of application.

## Instruction

Lectures and problem solving sessions. Laboratory work may occur as part of the project. Moreover, compulsory assignments may be given during the course.

## Assessment

Written examination (4 credit points) at the end of the course. Written project report (1 credit point).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.