Introduction to Major Applied Mathematics
ECTS Credits : /
Duration : 21 hours
Semester : S6
Person(s) in charge : Antoine Henrot
Key Words: Distribution theory, functional analysis
Prerequisites: the mathematical courses of the first year
Aims : provide some fundamental tools of analysis in order to start the basic courses of this major in good condition
Program and contents :
- Definition of distributions, examples: functions, Dirac measures. Convergence in the sense of distributions
- Derivative of a distribution of one variable, of several variable. Green formula and fundamental solution of the Laplacian. Differential equations and other equations in the space of distributions
- Fourier Transform of rapidly decreasing functions (Schwartz space). Space of tempered distributions, Fourier Transform of tempered distributions.. Properties, inversion formula. Application to the resolution of ordinary differential equations or partial differential equations. Computation of a Fourier Transform by residues.
- Complement of functional analysis for Hilbert spaces.