The course deals with the numerical solution of differential equations. First initial-value problems are studied (Runge-Kutta methods, linear multistep methods (especially Adams methods and backward differentiation methods), solution of stiff problems). Next solution methods for boundary value problems are introduced (the finite difference method, the control volume method and the finite element methods). The principles of those methods are explained for 1D second order boudary value problem. Main emphasis is placed on the finite element method in two dimensions. The following model problems are studied: elliptic (stationary heat transfer), parabolic (nonstationary heat transfer) and hyperbolic (membrane vibration including eigenproblems).