Département de Physique

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Introduction to probability (Course & exercises)
(ummto.faculté des sciences, 2025-12-16) ATIL, Lynda
This handout is intended for second-year Mathematics students, as part of the Numerical Analysis 2 module. This document is structured into four chapters: 1. Reminders and supplements on matrices: This chapter aims to recall and demonstrate a number of results related to matrices and vector spaces. 2.of finite dimension, and which will be constantly used throughout the rest of the handout. Numerical resolution of linear equation systems: We study direct methods (Gauss, Cholesky) that allow us to obtain the solution in a finite number of operations and iterative methods (Jacobi, Gauss-Seidel) that seek the solution step by step starting from an arbitrary initial vector to solve a linear system. 3. Calculation of eigenvalues and eigenvectors: This chapter covers methods for calculating approximations of the set of eigenvalues of a matrix A and the associated eigenvectors. 4. Associated eigenvectors. Numerical resolution of differential equations: "We address different numerical methods for the approximate solutions of ordinary differential equations."