209809 Erweiterungsmodul "Mathematical Modelling of Biological Systems - Introduction to Theory and Practice"" (V+Ü) (WiSe 2011/2012)

Course content
The aim of this course is to develop understanding of model development, analysis and validation through theoretical lectures and practical hands-on training in computer tutorials. Mathematical tools which will be introduced include ordinary differential equations, stability analysis, introduction to bifurcation theory and fundamental linear algebra. The mathematics will be introduced when needed for the analysis of a particular model so that new theoretical concepts are immediately applied
to a practical problem. During the course several prototype models will be thoroughly analysed exemplifying general phenomena such as bistability and oscillations and their mathematical foundation. By this, students will learn how to apply mathematical concepts to biological systems and discover the strength of the general mathematical approach by realising
that phenomena observed in completely different biological fields are based on the same fundamental principles.

Learning outcomes
By the end of the course the students are able to
- translate small biological systems into a theoretical description, such as sets of differential equations, Boolean networks, etc.
- implement these mathematical models in a modelling software
- analyse the models with the acquired techniques (stability analysis, bifurcation analysis etc.)
- validate the models by comparing them to experimental data
- perform simple parameter fits