Computer Visualization and Vector Calculus
Matthias Kawski
Department of Mathematics
Arizona State University
kawski@asu.edu
Abstract
This article demonstrates how newly available technology (e.g. the symbolic and graphical capabilities of MAPLE) leads to a complete rethinking how key concepts of (vector-) calculus are introduced. The new approach is accessible to a much broader population.
Single variable calculus has seen compelling changes in the last decade due to new technology. One should proceed in complete analogy on all levels of calculus -- here the focus is on vector calculus. Specifically, it is shown how to see local linearity (differentiability) and (uniform) local constancy (Riemann integrability) through appropriate zooming at all levels of calculus. Highlights are: How to see the divergence and curl by zooming, and a single, completely intuitive argument that applies to Stokes' theorem and all its cousins at all levels.
The proposed approach is implemented in MAPLE and has been extensively class-tested.
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