Differential Equations: A Universal Language

Author(s)

Bethany Caron, University of Rhode IslandFollow

Advisor

Montgomery, John [faculty advisor, Department of Mathematics]

Date

5-2008

Comments

The PNG and JPEG images require Windows Picture and Fax Viewer or similar program to open the files

Keywords

differential equations; math; model

Abstract

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” – David Hilbert Differential equations are equations of one or more variables that involve both functions and their derivatives. These equations have many applications to the everyday “non-math” world, including modeling in engineering, physics, biology, chemistry, and economics. Differential equations are used when a situation arises where one needs to study a continuously changing quantity (expressed as a function) and its rate of change (expressed through its derivatives). The solutions to differential equations are functions that make the original equation hold true, and they can give a plethora of information about the situation at hand. Through this project, I have gained valuable insight into how differential equations are used to model real life situations to make predictions and how powerful of a tool they can be. Only after creating and solving complex equations modeling situations applicable to physics, engineering, economics, and other areas of study, can one truly appreciate the utility and value of differential equations. Also, speaking with professionals in fields where these modeling situations are applicable, such as professors at URI and other authorities at private companies throughout Rhode Island, also leads one to understand the true significance of this fundamental area of mathematics. In speaking with these professionals, I have also learned to explain and interpret such a high level of mathematics in such a way that anyone not sufficient in math can understand.