The investigation of dynamical systems in mechanical, electrical or chemical engineering usually requires mathematical modeling of the system behavior. The object-oriented modeling language Modelica provides powerful features which make it possible to build up very complex even hybrid systems quite easily. But, what happens if a Modelica tool is not capable to compile and/or correctly simulate the system of interest? Reasons can be i.e. modeling errors, wrong parameter values and/or numerical instabilities. Automatic problem detection is usually not possible and only understanding of symbolical and numerical techniques behind the scene can help in resolving this issue.

This tutorial provides a basic understanding on the mathematical aspects of object-oriented modeling and simulation. Different phenomena are explained in detail using simple examples which can be thoroughly analyzed during hand-out exercises.