Introduction to mathematical modelling and simulation - Prüfungsnummer 9915450
Mathematical models play a major role in the understanding of physical, technical, biological and socio-cultural systems as well as for the prediction of their future development.
In order to analyse or to influence such a system, it is necessary to identify a suitable model first. With the help of such a model it is possible to perform non-expensive numerical experiments and to - at least approximately - simulate the “real-world”-behaviour of the system.
Therefore, the main objective of mathematical modelling is to find a suitable mathematical description, to set up the needed mathematical equations and to determine the corresponding parameters of the model.
In this course we will focus mainly on non-linear dynamical systems. For the investigation of these systems so-called state space models – based upon the solution of ordinary differential equations - will be used. Examples from different fields will be considered and simulations using MATLAB or Python will be carried out.
After completing this course the students are able to convert different problems from the natural and engineering sciences into a mathematical description. They know the fundamental principles of modelling and can apply them to a specific problem. The students can set up the corresponding equations and implement simple models on a computer.
The students are able to interpret and to validaHolgerte the simulation results. They can use these results to judge and to predict the behaviour of technical systems of different complexity.
- Basic principles of mathematical modelling
- Ordinary differential equations and state space models
- Linear dynamical systems
- Non-linear dynamical systems
- Deterministic chaotic behaviour
- Time series analysis and forecasting
Target audience: mathematically interested students.
Requirements: knowledge of differential equations and MATLAB or Python would be advantageous, but is not compulsory.
Dozent/in: Prof. Dr. Walter, Holger