Acquire the theoretical and practical backgrounds for the numerical approximation of ODEs and PDEs using standard numerical methods:
1) One-step methods for ODEs: introduction to ODES, Cauchy-Lipschitz theorem, development of numerical methods, convergence analysis
2) Finite difference method for usual linear PDEs: introduction to PDEs, principle of the finite difference method, application to Poisson and heat equations in 1D.
3) Finite element method for elliptic linear PDEs: variational formulation and Lax-Milgram theorem, variational approximation and convergence study, algorithmic implementation in 1D of Lagrange P1 finite elements.
4) Resolution of linear systems: basics of linear algebra, direct methods, iterative methods.