Physique mathématique [ LPHY2171 ]

Measure theory, distributions, Green's functions, spectral theory,
differential forms.

(Description):
- Concepts of topology
   * Euclidian
   * Connected space, topological group
- Measure theory and Lebesgue integral
   * Measurable space and functions
   * Lebesgue's integral
   * Applications to probabilities
- Distributions et Green's functions
   * Tests functions and distributions
   * Operations and Fourier transforms
   * Green's functions
   * Applications to partial differential equations
- Spectral theory in Hilbert's spaces
   * Elementary properties of Hilbert's spaces
   * Linear functional and operators
   * Spectra
   * Applications to polynomials and Quantum Mechanics
- Concepts of differential geometry
   * Manifolds and differential forms
   * Applications to thermodynamics and Relativity

This course introduces various mathematical structures widely used in
various theoretical and applied fields and necessary for the
physicists. The interest of these objects will be illustrated on
various concrete examples.