Difference equations: the constant-coefficient linear case. Runge-Kutta and Multistep methods for initial value Cauchy problems: consistency, convergence, stability, automatic step control. Finite difference approximations of initial and boundary value problems for elliptic, parabolic and hyperbolic PDEs. Explicit and implicit methods. Consistency, stability, convergence. An outline of finite element and finite volume methods. Practical Matlab exercises about the studied methods.