Bischof, G., & Steinmann, C., & Kainz, T., & Menard, E., & Poetsch, R., & Sterkl, M., & Tröster, C. (2022, August), Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems  Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--40535

\bibitem{asee_peer_40535}
  Bischof, G., \& Steinmann, C., \& Kainz, T., \& Menard, E., \& Poetsch, R., \& Sterkl, M., \& Tröster, C. (2022, August), \emph{Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems}
  Paper presented at 2022 ASEE Annual Conference \& Exposition, Minneapolis, MN.
  10.18260/1-2--40535

Guenter Bischof, Christian Steinmann, Thomas Kainz, Eric Menard, Robert Poetsch, Maximilian Sterkl, and Christoph Tröster.  "Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems".  2022 ASEE Annual Conference & Exposition, Minneapolis, MN, 2022, August.  ASEE Conferences, 2022.  https://peer.asee.org/40535 Internet.  15 May, 2024

\bibitem{asee_peer_40535}
  Guenter Bischof, Christian Steinmann, Thomas Kainz, Eric Menard, Robert Poetsch, Maximilian Sterkl, and Christoph Tröster.
  "Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems".
  \emph{2022 ASEE Annual Conference \& Exposition, Minneapolis, MN, 2022, August}.
  ASEE Conferences, 2022.
  https://peer.asee.org/40535 Internet.  15 May, 2024

@INPROCEEDINGS{asee_peer_40535
author = "Guenter Bischof, Christian Steinmann, Thomas Kainz, Eric Menard, Robert Poetsch, Maximilian Sterkl, and Christoph Tröster"
title = "Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems"
booktitle = "2022 ASEE Annual Conference \& Exposition"
year = "2022"
month = "August"
address = "Minneapolis, MN"
publisher = "ASEE Conferences"
note = {https://peer.asee.org/40535}
number = {10.18260/1-2--40535}
}

TY  - CPAPER
AB  - The use of technology in the teaching and learning of mathematics is becoming increasingly more prevalent in mathematics education. It affects not only how to teach mathematics, but also what mathematics becomes possible to be taught. Especially commercially available computer algebra systems have become ubiquitous tools, although there is some concern that they may detract students from understanding core mathematical concepts. Such an undesirable effect can be avoided by making use of high-level programming languages in mathematics education. Computer programming does not only strengthen problem solving skills and logical and sequential reasoning, it also provides a high degree of flexibility and an ample scope for applications in teaching and learning.   
Here we present an example of the synergistic effect of the interaction of computer programming and mathematics in undergraduate engineering education within the framework of team-oriented project-based learning. The students of an Engineering Mathematics course were organized into teams of three and given the task to develop computer programs that make use of mathematical algorithms taught in this course. Two teams chose the simulation of the behavior of a non-linear dynamic system, namely a mathematical pendulum with an elastic suspension. The teams were required to solve the equations of motion numerically and to visualize the motion of the system by making use of a high-level programming language. The students were given free rein on creativity, which lead to equivalent computational results but significantly different visualization designs. One group used C# as programming language and chose a rather scientific approach. Their program offers several options like phase space visualizations and the comparison of different numerical methods with varying orders of the truncation error. The other group used the Unity game engine for the visualization of an elastic pendulum with three degrees of freedom. The motion of the system can be observed on the computer monitor or through a virtual reality viewer as a three-dimensional object in an immersive, virtual environment. By using a VR headset, the users have the possibility to move around the virtual environment – a huge pendulum hall – and immerse themselves into the spatial perception of the moving spring pendulum. 
In this paper we present our teaching approach, the theoretical background and the outcome of the student projects. The different solution and visualization strategies of the student teams are contrasted with each other and discussed. The programs can be obtained from the authors free of charge. 

AU  - Guenter Bischof
AU  - Christian Steinmann
AU  - Thomas Kainz
AU  - Eric Menard
AU  - Robert Poetsch
AU  - Maximilian Sterkl
AU  - Christoph Tröster
CY  - Minneapolis, MN
DA  - 2022/08/23
PB  - ASEE Conferences
TI  - Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems
UR  - https://peer.asee.org/40535
DO  - 10.18260/1-2--40535
ER  -