Transform Methods

5 credits

Syllabus, Bachelor's level, 1MA034

A revised version of the syllabus is available.

Code: 1MA034
Education cycle: First cycle
Main field(s) of study and in-depth level: Mathematics G1F
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

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

Learning outcomes

In order to pass the course (grade 3) 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;

apply transformation rules to compute the transforms of simple functions, and 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 complete ON-system and be familiar with the theorems of Parseval and Plancherel;

use transforms as a technique for solving differential equations and difference equations;

formulate important results and theorems covered by the course;

use the theory, methods and techniques of the course to solve mathematical problems;

present mathematical arguments to others.

Content

The Laplace transform, the z-transform, Fourier coefficients and Fourier series. Briefly about the Fourier transform. Applications to ordinary and partial differential equations.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.