Entry requirements

60 credit points Mathematics including Transform Methods, Linear Algebra II

Learning outcomes

In order to pass the course (grade 3) the student should

• understand the distinction between pointwise and uniform convergence and be able to decide whether a given sequence of functions is uniformly convergent;
• know the properties of the Fejér and Dirichlet kernels;
• know some sufficient conditions for pointwise and uniform convergence of Fourier series;
• be able to give an account of the theory of complete orthogonal systems and know how to apply it to Fourier series;
• be familiar with the rules for Fourier transformation and know how to apply them;
• be familiar with the L²-theory for the Fourier transform;
• know how to define and apply the discrete Fourier transform;
• be able to formulate important results and theorems covered by the course and to describe the main features of the proofs of important theorems;
• be able to use the theory, methods and techniques of the course to solve mathematical problems;
• be able to present mathematical arguments to others.

Content

Series of functions, uniform convergence. Fourier series: convergence theorems and L²-theory. Orthogonal systems. The Fourier transform. Applications to ordinary and partial differential equations. The discrete Fourier transform, the fast Fourier transform.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.