Abstract

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Researchers should cite this work as follows:

• Kowalczyk, R. (2023). 1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data. SIMIODE, QUBES Educational Resources. doi:10.25334/9SC3-2254

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Article Context

Description

Kowalczyk, Robert E.  and Adam O. Hausknecht. 1999. Using Differential Equations to Model Real-World Data. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics.  Reading MA: Addison-Wesley Publishing Co. pp. 246-250.

http://www.math.umassd.edu/~ahausknecht/aohWebSiteFall2022/temath2017/TEMATH2/Presentations/Articles/1997ICTCMProceedingsWeb.pdf . Accessed 30 March 2023.

Opening of article, “With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations. Rather than have our students passively study a cookbook collection of special techniques for solving a few types of differential equations, we now have them actively involved in designing models and testing them with real-world data. Real-world data provides an extremely rich environment for developing, learning, and applying differential equations. Government sources, laboratory experiments, and research studies present a wealth of data that can be modeled by differential equations. Additionally, with the availability of sensors that attach to a computer or a graphing calculator, it has become an easy task to gather data from many different types of physical experiments. Thus, it has become common practice for our students to not only develop and test their own models, but, to test the validity and accuracy of the many differential equation models that are presented in a standard first year course. By seeing for themselves how well differential equations model physical phenomenon, they build up confidence in using differential equations in their studies, research, and future careers. In our courses, we emphasize the fact that not only do we want a model that fits the data well, but we want one that also makes sense from a theoretical and realistic point of view. Many models fit data well over a short time period (the data looks linear), but over longer time periods and for purposes of making projections into the future, one model may be much more appropriate than the others. We now present a few examples that use differential equations to model real world data.”

There follow examples (but with not data) on Hooke’s Law for Simple Harmonic Oscillator, although the glucose tolerance test piece does offer data.

Keywords: Hooke’s Law, harmonic oscillator, calculator, glucose, glucose tolerance test, data, Torricelli’s Law, RC circuit, circuit