Fourier Analysis

This course provides an introduction to Fourier analysis for functions of one real variable.

The following topics are treated:

• Fourier series of periodic functions that are absolutely integrable: basic properties, convergence results, and applications to partial differential equations (PDEs)

• Fourier transform of absolute and square integrable functions: basic properties, inversion formulas, the Poisson summation formula, and the Shannon sampling theorem

• Discrete Fourier transform (DFT): theory and computational aspects.

The exam consists in an oral exam.

There will be weekly homework assignments. Students who acquire at least 70% of the points attainable by doing the weekly problem sheets are given an additive bonus of 0.5 on their final grade (e.g. grade 8 (without bonus) will be grade 8.5 (with bonus)).

Disclaimer: information may change depending on unforeseen circumstances or measures (see: TER Art 29, sub 4).

In case of insufficient results a repair option may exist in accordance with Article 2, Examination requirements, Clause 4, of the Implementation Regulations 2024-2025.