Introduction to Differential and Difference Equations through Modeling

By: William P. Fox

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eText | 9 July 2025 | Edition Number 1

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This book presents an opportunity to learn difference and differential equations through a modeling-first approach. The text is meant as an introduction to those equations and not as a text only for modeling courses. No previous exposure to these equations is expected. Modeling in Introduction to Differential and Difference Equations through Modeling is presented as the vehicle for learning difference and differential equations.

Although the topics in difference and differential equations are consistent with those in other textbooks, this approach differs. The presentation starts with a model (or several models) and offers the solution with minor discussions. Then, methods to obtain those solutions are presented and show these same models and others again in more detail.

This approach is designed to focus on the use of difference and differential equations to solve real-world problems, and to learn not only these primary topics, but how to apply these through modeling.

The authors begin with a review of matrix algebra, then an introduction to modeling. The text progresses to discrete dynamical systems, and then to the standard organization of most differential equation texts, making the alignment with a current syllabus easier.

Technology is a significant modeling component. Excel®, Python®, and Maple® are presented as methods to solving the models. This material has been class tested at the US Military Academy at West Point, Marian University, the College of William & Mary, and the Naval Postgraduate School with great success.