The first part introduces the most important discretization methods for ordinary and partial differential equations. On the one hand we discuss well known methods like the Euler method or the Runge Kutta methods. On the other hand also more advanced topics like adaptivity or mixed problems are treated.

The second part deals with unstable numerical methods for non-linear ordinary differential equations. The connection between dynamical systems and iteration theory is presented. One highlight is for example the relation between the Euler method and Julia sets.

Inverse problems are the subject for the third part. In many applictions inverse problems for differential equations have to be solved. The lecture gives an introduction and shows how the arising unstable problems can be solved.

The summer school will be completed by a social program. Here, the students will obtain some information about germany, epecially about the german university system. Moreover, a comprehensive sports program is planned.

In practical exercises some of the algorithms will be implemented in MATLAB. Therefore we also give a short introduction to MATLAB.

The summer school is aimed for master students or PhD students at the beginning of their thesis. Some experience with ordinary differential equations and numerical analysis will be useful, but is not required.