Modelling, Simulation and Visualization (3 ECTS)

Objective

Knowledge and understanding:
The students will learn how to solve basic mathematical problems with Maple on the computer. They are able to differentiate or integrate a function, to solve equations and differential equations, and to graphically display functions by means of graphs, 3D plots and animations.

Skills:
The students are able to compute the Fourier series of a signal with Maple to perform a signal analysis. They are also able to analyze non-periodic signals applying the Fourier transform.

Content

We will start with an introduction to the computer program Maple. With only few commands, we are able to display or animate, to visualize in 3D or to animate in 3D physical and engineering expressions. In the next step, we will directly apply a method to model electric circuits that consist of R- (Resistor), L- (Inductor) or C- (Capacitor) elements in case of an AC voltage. With this method we can model any kind of circuits that consist of as many elements as necessary.

We will continue the lecture with the modeling of the time behavior the electrical systems. This is done by the setup of ordinary differential equations. With the help of Maple, we solve these differential equations numerically in order to get the impulse response. Finally, with its visualization tools we visualize the time behavior of the systems.

The last part of the lecture is related to the system analysis by means of the frequency analysis. Using system routines like FFT we identify the frequency behavior of systems. Once again by visualizing the results we identify the relations between frequency analysis and system theory: impulse signal, impulse response, transfer function, and system function.

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

More than 50% of points

Assessment criteria, good (3)

More than 70% of points

Assessment criteria, excellent (5)

More than 90% of points

Assessment criteria, approved/failed

40% of points

Qualifications

Basic mathematics and complex numbers, basic programming skills

Further information

Intensive course with hands-on exercises on paper and with the computer.
A computer with Maple (Student trial version) is required.

Webpage for the course: http://www.home.hs-karlsruhe.de/~weth0002/
-> Veranstaltungen -> Block-Veranstaltungen -> Modelling, Simulation, Visualization

Further information

Intensive course with hands-on exercises on paper and with the computer.
A computer with Maple (Student trial version) is required.

Webpage for the course: http://www.home.hs-karlsruhe.de/~weth0002/
-> Veranstaltungen -> Block-Veranstaltungen -> Modelling, Simulation, Visualization