How to teach dynamical systems in engineering from a mathematical point of view

Engineering products are often dynamical systems or they at least contain dynamical subsystems. Typical examples are rotating or oscillating parts of devices, moving robots or streams in electrical circuits. Modelling and simulation is used nowadays to predict and control the behaviour of these complex systems. The essential part of such mathematical models can often be described by a first order system of differential equations. By using professional software like MATLAB and SIMULINK, one can generate motion trajectories in the state space of the system. Simulations can be made to study the change of trajectories dependent on parameter choices and input quantities. Before the practical use of the systems, speed and reliability investigations are necessary in order to avoid ineffectiveness and damage in the practical application. The importance of efficiency studies, error estimations and stability considerations given the underlying numerical algorithms is discussed. Hints are also provided on how to check whether the computer results are correct or not.