Modeling a Changing World
The world is dynamic and often modeled using differential equations. This article uses modeling to motivate the need for numerically solving ordinary differential equations. The article discusses such applications as a mass-spring system and its connection to computer simulation for movies. An interactive applet that simulates a two-body gravitational model of the moon and earth allows for exploring the topic of numerical error. Other applets explore topics that include slope fields, numerical integration and numerical solvers for ordinary differential equations.
About the Authors
Timothy Chartier is an Assistant Professor of Mathematics at Davidson College. Tim holds a bachelors degree in Applied Mathematics and a masters degree in Computational Mathematics from Western Michigan University. He received his doctorate in Applied Mathematics from the University of Colorado at Boulder. His research area is numerical analysis. In his time apart from academia, Tim enjoys the performing arts, mountain biking, nature walks and hikes, and spending time with his wife and two children.
Nicholas Dovidio majored in Mathematics with a concentration in Computer Science and graduated with honors in 2007 from Davidson College. Currently, Nick is a graduate student in Computer Science at Stanford University. He is an avid fencer and has competed at national levels.
Technologies used in this article
This article is in the form of a Java Archive (JAR) file. You will need the Java plug-in installed in your browser.
To open the article, click on the link below, and when prompted, save the JAR file to your local computer. Then launch the JAR file. If you open the article directly with your browser, your security settings may keep the applets from working properly.