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Bringing differential equations to life by two- and three-dimensional visualizations of numerically simulated dynamic systems

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Conference

2022 ASEE Annual Conference & Exposition

Location

Minneapolis, MN

Publication Date

August 23, 2022

Start Date

June 26, 2022

End Date

June 29, 2022

Conference Session

Incorporating Technology in the Classroom

Page Count

16

DOI

10.18260/1-2--40535

Permanent URL

https://peer.asee.org/40535

Download Count

393

Paper Authors

biography

Guenter Bischof Joanneum

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Günter Bischof holds a doctorate in physics and is currently an Associate Professor of Applied Mathematics at the University of Applied Sciences FH Joanneum in Graz.

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Christian Steinmann

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Christian Steinmann is manager of HM&S IT-Consulting and provides services for Automotive SPiCE.
Currently, his main occupation is process improvement for embedded software development for an automobile manufacturer. On Fridays, he is teaching computer science and programming courses at Joanneum
University of Applied Sciences in Graz, Austria.

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biography

Thomas Kainz

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Thomas Kainz is an undergraduate automotive engineering student at the University of Applied Sciences FH Joanneum in Graz, Austria. Previously he finished the International Baccalaureate Diploma Programme at the Graz-International-Bilingual-School (GIBS) in Graz, Austria.

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Eric Menard

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Eric Menard is an undergraduate automotive engineering student at the University of Applied Sciences Joanneum Graz. He is partaking in the formula student program to develop electric racing vehicles. Previously he was a student at the higher technical institute Lastenstraße in Carinthia (Austria) where he graduated in the field of electrical engineering.

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Robert Poetsch

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Robert Poetsch is currently studying Automotive Engineering at the University of Applied Sciences Joanneum in Graz.
Before this he graduated in electronics and IT from the Higher Technical College in Mödling.

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Maximilian Sterkl

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Maximilian Sterkl graduated from a Higher Institute of Technical Education and worked as a internal quality engineer at a company producing elevator safety parts, before starting to study at the University of Applied Sciences FH Joanneum.

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Christoph Tröster

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Christoph Tröster is currently studying Automotive Engineering at the University of Applied Sciences Joanneum in Graz. After completion of his studies, he would like to participate in the development of electric cars.

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Abstract

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.

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

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