Pull-Back Cars: Vehicles for the Instruction of Differential Equations

Abstract

This article develops a mathematical model for the motion of toy pull-back cars that can be introduced and revisited throughout an undergraduate differential equations course. This survey of the pull-back car modeling scenario enables students to connect course content with real-world experiences and experimental data, while leaving room for further exploration and advancement of the model.

Acknowledgment

The authors wish to thank Brian Winkel, Director of SIMIODE, for connecting the authors based on their shared interest in the mathematical modeling of pull-back cars and for providing helpful feedback on an early draft of this article.

Additional information

Notes on contributors

Tova Brown

Tova Brown ([email protected]) is an assistant professor of mathematics at Wisconsin Lutheran College in Milwaukee. Her Ph.D. from the University of Arizona in 2016 was focused on pure mathematics, and in the years since then her interest in mathematical modeling has been steadily growing. She first became interested in the problem of modeling toy pull-back cars because of her son’s interest in playing with them.

Brody Johnson

Brody Johnson ([email protected]) spent the first six years of his academic career as a student of mechanical engineering before pursuing graduate study in mathematics at Washington University in St. Louis. He earned his Ph.D. in mathematics in 2002 under the tutelage of Guido Weiss and is now a faculty member at Saint Louis University, where his background in engineering continues to influence both his research and teaching efforts.