Falling Water: A Modeling Story

Abstract

A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the development of various types of separable equations. Finally, survey data of the student experience of modeling indicates a general appreciation for modeling tasks such as this and a positive indication of their educational value.