Formation M1 Fundamental and applied mathematics
Semester2
Teaching staffLecturer : Jean-Marc Delort, Thomas Duyckaerts, Vuk Mlisic, Francis Nier , TA :
Credits 6 ECTS
Teaching hours 30h of lectures + 30h of TA sessions
Validation schemeFinal exam

Syllabus

The first half of the course is a core curriculum; we then offer two options.

Common core: Series and Fourier transform. Hilbertian theory of the Fourier series, Sobolev spaces on the torus. Fourier transform, Schwartz space and its dual space of temperate distributions.

Fundamental option: Distributions. Topologies on regular function spaces. Distributions on an open space in Euclidean space. Convolution. Elementary solutions of partial differential equations with constant coefficients and applications.

Applied option: Signal processing. Discrete Fourier transform. Fast Fourier transform. Sampling. Shannon's theorem. Analog and discrete filters.

Prerequisites

Measurement theory, elementary analysis, and topology of license metric spaces.