Preliminaries ( 7 hours of Lectures +1 hour of Exercise session)
Complex functions, topology of complex field, sequences and series.
Complex analysis (20 hours of Lectures + 4 hours of Exercise session)
Cauchy integral theorem, analyticity of holomorphic functions, Laurent series, study of isolated singularities, Residue theorems and application to calculus of real integrals. Different notion of integrability.
Functional analysis and Fourier series (15 hours of Lectures + 3 hours of Exercise session)
Metric spaces, Banach spaces, Hilbert spaces, Fourier series in an Hilbert space. Pointwise convergence of the Trigonometric Fourier serie.
Laplace transform (6 hours of lectures+ 1 hour of Exercise session)
Definition of Laplace transform and main properties. Application to ODE.
Fourier transform (6 hours of Lectures + 1 hour of Exercise session)
Definition of Fourier transform and main properties.
Distribution(5 hours of Lectures + 1 hour of Exercise session)
Definition of distribution, main properties and Fourier transform of a distribution.
A short introduction to PDE (3 hours of Lectures)