The aim of the course is to teach basics computational methods for solving simple and common mathematical problems by computers and numerical software. This includes the construction, application and analysis of basic computational algorithms. Problemsolving by computers is a central part of the course.

Mathematical models are often written as systems of linear and nonlinear equations and differential equations. Students are expected to discretize such equations, that is to construct computable approximations. Moreover, students have to implement and to apply such algorithms independently

Contents

Linear systems, matrix factirizations and condition, least squares, orthogonal systems, L"-approximation, (Newton-) iteration and order of convergence, interpolation, quadratur, discretization of initial value problems, stiff and non-stiff problems, basics of finite elements, best approximation, error estimates.