2013-HuberEtAl-Teaching Differential Equations With Modeling. Notes from JMM 2013 Minicourse.
From the preface, “Mathematical modeling has been an important part of our differential equations courses for many years and we appreciate the opportunity to share our passion and ideas with you. We hope that you find the projects in this booklet entertaining, thought provoking, and most of all, useful in your differential equations course. Feel free to use these projects as they are or to modify them to better reflect the interests and abilities of your students."
The projects in this booklet in many ways reflect the interests and backgrounds of the authors. Who but a former Airborne officer teaching mathematics at West Point would dare to write a differential equations project about parachuting? All of us see mathematics in general, and differential equations in particular, as a way to describe the changing world around us. And we use these inspirations to construct demonstrations and projects for our students in the hopes that one day they will share the excitement and joy of modeling a natural (or sometimes supernatural) phenomenon and using mathematics to understand it in a deeper and more fulfilling manner.
Most of these projects are organized in a similar fashion. We begin with an introduction to the problem, outline or construct the mathematical model, and then lead the student through a sequence of steps to solve and analyze the model. In some cases, the focus of the project is more on the development of the model equations. In these projects we generally outline how differential equations are used to model phenomena of this type and then guide the student through the modeling development process.”
There are 18 complete projects which should spawn other ideas for Modeling Scenarios in SIMIODE.
Keywords: differential equation, model, teaching, project
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