Department of Mathematics

Lecturer	Brahim ABDELMALEK
Information	Master - Applied Mathematics Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/930 Semester : S1 Unit : UEF1 Credit : 9 Coefficient: 5
Content	Chapter 1. Test functions, regularization, density theorems. Distributions: definition, derivation, multiplication by a function, restriction and support, convergence, regularization. Fourier series expansion of a periodic distribution. Chapter 2. Surface measurement on a closed hypersurface of Euclidean space, formula for jumps with several variables, formula for integration by parts. Chapter 3. Convolution of distributions, elementary solutions of Laplacian, applications to the theory of harmonic functions: maximum principle, Liouville\'s theorem. Chapter 4. Fourier transform of tempered distributions, applications to the search for tempered solutions of partial differential equations, elliptic regularity theorem. Chapter 5. One- and multi-variable Sobolev spaces, application to the solution of the Dirichlet problem: existence and regularity.
Evaluation	- Final exam = 67% - Continuous work (33%) = Micro interrogation (10 points) + Participation and Attendance (05 points) + Homework (05 points).