Modelling and Simulation

- Introduction to mathematical modelling (notions and notations, fields of application, derivation of models, analysis of models, classification of models, scales and hierarchy) - Discrete modelling and simulation (decision models: games, strategies, elections; scheduling problems; discrete event simulation: data and job traffic; neural networks) - Continuous modelling and simulation (population dynamics: models and their numerical treatment; control: deterministic and fuzzy logic approaches; traffic flow: modelling via continuous quantities; heat conduction: models and their numerical treatment) - Modelling in software design (optional; basic concepts, description techniques, methodology)

The participants are able to develop and to assess formal (mathematical or infomatical) model concepts for a verbally described problem. They can select and apply successfully strategies for simulation, i.e., the computer-aided solution of these models. They know exemplary important model classes and can develop own solution procedures for simple scenarios.

MA0901 Linear Algebra for Informatics, MA0902 Analysis for Informatics, IN0019 Numerical Programming

This module comprises lectures and accompanying tutorials. The contents of the lectures will be taught by talks and presentations. Students will be encouraged to study literature and to get involved with the topics in depth. In the tutorials, concrete problems will be solved - partially in teamwork - and selected examples will be discussed.

Slides, whiteboard, exercise sheets

- Bungartz, Zimmer, Buchholz, Pflüger: Modellbildung und Simulation - eine anwendungsorientierte Einführung, Springer, 2009 - Fowkes, Mahoney: Einführung in die mathematische Modellierung, Spektrum,1996 - Gander, Hrebicek: Solving Problems in Scientific Computing Using Maple and MATLAB, Springer, 1997 - Bossel: Modellbildung und Simulation, Vieweg, 1994 - Banks et al.: Discrete Event System Simulation, Prentice Hall, 1996 - Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993 - Nauck, Klawonn, Kruse: Neuronale Netze und Fuzzy-Systeme, Vieweg, 1994

Type of Assessment: exam In the exam students should prove to be able to identify a given problem and find solutions within limited time. The examination will completely cover the content of the lectures. The answers will require own formulations. In addition, questions requiring short calculations may be posed. Exam questions check the ability to develop and to assess formal (mathematical or informatical) model concepts for a verbally described problem. The assignments test whether the participants are able to select and apply successfully strategies for simulation. Exam tasks evaluate the students' knowledge on important model classes and corresponding solution procedures for simple scenarios.