Introduction to linear algebra: vectors and matrices, solving systems of linear equations, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and eigenvectors, singular value decomposition and linear transformations. Applications in and links to computer science will be presented in parallel.

The central topic of this course is the numerical treatment of ordinary differential equations. It focuses on the derivation, analysis, efficient implementation, and practical application of single step methods and pay particular attention to structure preservation.

This course gives an introduction to numerical methods. It covers nonlinear algebraich equations, quadrature and initial vaule problems. The focus is on the ability to apply the numerical methods.

The aim of this course is to show how numerical algorithms are implemented correctly and efficiently.We follow this agenda by discussing various important algorithms of numerical linear algebra.