This course is divided into two parts. The first is devoted to methods for solving continuous optimization problems. More specifically, the aim is to determine the minimum or maximum of a continuous function, linear or not, on a subset of R^n (where R denotes the set of real numbers and n is a given integer representing the dimension of the space under consideration), with or without constraints. Practical exercises, based on programs written in C to be completed, illustrate these methods. The second part deals with two classic problems in numerical analysis: solving linear systems and calculating the eigenvalues and eigenvectors of linear applications.