Modeling and simulation

In the course Modeling and Simulation, basic methods for mathematical modeling and simulation of technical systems are presented. In the first part of the lecture, mathematical modeling is introduced using natural laws and principles. Selected systems from the various fields of engineering are modeled and the governing equations are derived.

The second part of the lecture deals with the techniques of scientific computing and mathematical simulation in Python. First, the basics of the common functions in Python and the packages numpy, scipy and pandas are introduced. Subsequently, time-independent simulations (systems of equations) and continuous-time simulations (initial value problems) are carried out using the packages presented. Finally, discrete-event simulations (graph theory, Markov chains, queueing theory) are discussed.

• Introduction to mathematical modeling (concepts, applications, derivation and analysis, classification)
  • Fundamentals of systems theory
  • Principles of mechanics
  • Kirchhoff's laws
  • Traffic flow modeling
• Fundamentals of scientific computing, numerics and analysis
  • Basic operations in a common numerical environment
  • Graphical representation
  • Linear & non-linear systems of equations, eigenvalue problems
  • Distribution densities, correlations, FFT, filtering
• Continuous modeling and simulation
  • Nonlinear systems of equations
  • Initial value problems (problem definition, basic concepts, simple single-step methods)
  • Boundary value problems (problem definition, basic concepts, simple FD discretization)
• Discrete-event simulation
  • Graph theory
  • Markov chains
  • Queueing theory

The contents of the lectures Mathematics 1-3, Engineering Mechanics 1-2, Electrical Engineering and Electronics, Materials Engineering and Computer Science are assumed.