Electronic Proceedings of the Twenty-first Annual International Conference on Technology in Collegiate Mathematics

New Orleans, Louisiana, March 12-15, 2009

Paper S037

This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Twenty-first Annual International Conference on Technology in Collegiate Mathematics, ISBN 0-321-68983-6, Copyright (C) 2010 by Pearson Education, Inc.


A More Favorable Role for Piecewise-defined Functions in Calculus

Dennis Pence


Western Michigan University

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ABSTRACT

Usually piecewise-defined functions only play the role of a 'bad' character in calculus courses by illustrating discontinuity. Modern technology (both with graphing and symbolic algebra) makes it easy to include examples where piecewise-defined functions play a very positive role in the modern world. Calculus techniques do apply to these functions with some care. Topics will include Bézier curves, price functions that offer discounted prices for larger orders, and progressive tax functions. Even the topics of the trapezoid rule and Simpson's rule can be explained in terms of piecewise-defined approximating functions. We can even look at simple differential equations with a 'step-function' for a forcing term as the engineers often do.

Keyword(s): calculus