Using the Taylor Center to Teach ODEs

Authors

Alexander Gofen

Publication Date

11-27-2012

Keywords

Automatic differentiation; Dynamic graphics; Numerical pitfalls; Software; 3Dstereo

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://taylorcenter.org/Gofen/) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D stereo vision). After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration. The article therefore continues the thesis of Borrelli and Coleman (CODEE Journal, http://www.codee.org/ref/CJ09-0157) that awareness and caution are needed while interpreting the results of numeric integration. We offer practical ideas and advice on how to use the Taylor Center for teaching ODEs, and to increase the motivation and interest of students.

Note: This article was revised on Sep 1, 2020 to reflect an address change of http://www.ski.org/gofen/ to http://taylorcenter.org/Gofen/

Recommended Citation

Gofen, Alexander (2012) "Using the Taylor Center to Teach ODEs," CODEE Journal: Vol. 9, Article 6.
Available at: https://scholarship.claremont.edu/codee/vol9/iss1/6