Textbook in PDF format Direct methods Introduction Gaussian elimination and the LR-decomposition The Cholesky decomposition The QR-decomposition (supplement) Eigenvalue problems Concepts and de nitions The von-Mises iteration The inverse iteration of Wielandt The LR-method and the QR-method for eigenvalue problems (Supplement) Householder's method of reduction to Hessenberg resp tridiagonal matrix shape (Supplement) Linear Programming (or Linear Optimization) Error analysis Introduction Propagation of errors in systems of linear equations Newton method Numerical quadrature Introduction The trapezoidal rule and the rectangle rule Quadrature formulas based on interpolation Newton-Côtes formula Numerical solutions of initial value problems Introduction Introduction to the solution theory of initial value problems Euler's method One-step methods - De nitions and elementary properties The method of Taylor comparison Runge-Kutta-methods of consistency order General Runge-Kutta methods Convergence of one-step methods and an error estimate Final remarks Finite di erences for boundary value problems Discretization for boundary value problems for ordinary di erential equations Discretization of boundary value problems for partial di erential equations Finite Elements Weak formulations of boundary value problems Ritz-Galerkin approximation Implementation of the Ritz-Galerkin method