Using the Taylor Center to Teach ODEs

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://www.ski.org/gofen/TaylorMethod.htm) 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 [2] 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.