Numerical solution of partial differential equations and applications

This document is a basis written in LaTeX for the lecture "Numerical Solutions of PDEs and applications" in the summer semester 2024
The objective of this course is to provide MMATH (all tracks) and MSE-M students at the University of Luxembourg with a global overview of two fundamental discretization methods to solve linear PDEs with boundary conditions: the finite element and finite difference methods. Not only the mathematical foundations will be developed but also their concrete implementation in view of their application to industrial mathematical problems. Simple problems will be fully solved using Python, paving the way to the understanding of more advanced methods.