Here you can find my notes taken in the course of Numerical Methods applied to Partial and ordinary Differential Equations. Sorry but the notes are in French! 

A century ago, mathematicians were working to find analytical solutions to equations proposed by physicists and mechanics. Sometimes, the complexity of these equations was so complex that they put a lot of energy in simplifying these models in order to obtain simpler ones for which the available tools, such as simpler ones for which the available tools, in particular complex analysis, could work, could work. These considerable contributions constituted the working capital of the in-engineer's working capital. However, they soon proved to be insufficient and it is only with the appearance of the first the appearance of the first computers in the middle of the XXth century, that another way, much more more promising and complementary way was born: it is the numerical analysis. 

The first problems were obtained by discretization of partial differential equations using the using the famous finite difference method. This made it possible to reduce the problem to the resolution of of a matrix system. Very quickly, the limits of this method appeared mainly because of the complex geometries, the heterogeneous media and the various boundary conditions that that the engineer wanted to introduce in his models. The arrival of the finite element method elements method brought an efficient and pleasant solution to all these problems and transformed all the transformed all the partial differential equation models of physics into matrix systems systems (linear or not). The purpose of this course is to give the main methods available to the scientist available to the scientist to solve these systems.

We followed a theoretical training and then moved on to numerical simulations on Python