Introduction to numerical methods used for analyzing and optimizing mechanical systems. General principles of numerical calculations, machine numbers, error estimation, numerical stability. Linear algebra: Cholesky-decomposition, Gaussian elimination, LU-decomposition, QR-decomposition, iterative methods, least square problems. Eigenvalue problem: general basics, normal forms, power method, QR-algorithm, computation of eigenvectors. Initial value problem: ordinary differential equations, Runge-Kutta methods with step size control, extrapolation methods, linear multistep methods, -applications. Programme libraries for optimization of mechanical systems, comparison of methods for analytical investigations with computational methods. The lecture is supplemented by computer exercises.