We will present the most common methods to approximate solutions to partial differential equations. Rather than giving an exhaustive list of the most efficient methods used in industrial codes, we will describe the mathematical foundations for the setting and the analysis of the principal methods. Some of them will be implemented with Matlab.
Chapter 1. Basics on the theory of linear PDEs, and finite difference methods. Chapter 2. Finite element methods for elliptic problems Chapter 3. Numerical approximation for hyperbolic equations