This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

dercex is a six line Mathematica program which, when used in conjunction with an algebraic technique accessible to calculus-level undergraduates, generates the Taylor Series solution to literally all ODE's in an undergraduate course (i.e., one given from Boyce & DiPrima, Ross, or Martin). In a first ODE course the program can be used as a capstone to show "universal" applicability of the fundamental existence theorem, or can be taught at the beginning of the course and used for numerical explorations. Particularly pertinent is the ability to create accuracy by increasing degree of the approximating Taylor polynomial or decreasing the size of the interval over which it is applied. Also, "general" solutions (actually the dynamical system associated with the ODE) can be created by treating problems symbolically.

G. Edgar Parker
Department of Mathematics
James Madison University
Harrisonburg, VA 22807
(540)568-6938
gparker@math.jmu.edu