Electronic Proceedings of the Seventh Annual International Conference on Technology in Collegiate Mathematics
Orlando, Florida, November 17-20, 1994
Using Spreadsheets and DERIVE to Teach Differential Equations
Department of Mathematics and Computer Science
Salisbury State University
Salisbury, MD 21801
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Another sticking point in the first semester Differential Equations course are solutions expressed in terms of definite integrals which must be approximated. Students do not believe that, for example, when asked to solve the initial value problem:
y'' - y = 1/x; y(1) = 0 y'(1) = -2that
y(x) = e^(1-x) - e^(x-1) + e^x Integral from 1 to x e^(-t)/t dt - e^-x Integral from 1 to x e^t/t dtis an acceptable answer and every bit as legitimate a function of x as sin(x). However, even a relatively simple to learn computer algebra package like DERIVE can graph functions defined this way. In this instance, a picture is truly worth a thousand words. students who see a graph of this function are much more inclined to believe than ones who are shown how to use Simpson's rule to compute a few values. In fact, using DERIVE they can do both.
In this paper directions for programming a spreadsheet to approximate solutions to first order differential equations will be given and their efficacy in teaching will be discussed. Also use of DERIVE to graph direction fields, to approximate solutions, to graph functions defined by definite integrals and to help with tedious algebra will be discussed.