This course provides basic training in analysis. This module enables students to master the mathematical tools used in applied mathematics, physics, mechanics and economics. It paves the way for third-year advanced mathematics programs.
The course introduces the formalism of distributions, introduced by Laurent Schwartz in the late 1940s, which provides a natural framework for the study of Fourier transformation. It then focuses on the study of the fundamental properties of the main partial differential equations of mathematical physics
- Distributions, derivation, convolution, regularization.
- Fourier series and transformations.
- Poisson and Laplace equations. Harmonic functions.
- Heat equation.
- Wave and Schrödinger equations.
F. Golse: "Distributions, analyse de Fourier et équations aux dérivées partielles"
Appendix "Intégration sur les surfaces"
Course language : French
- Teaching coordinator: Golse François
- Teaching coordinator: Jendrej Jacek