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Animating Calculus

by Ed Packel and Stan Wagon
Springer Verlag New York: published by TELOS, 1997, xiv+292 p
ISBN 0 387 94748 5 (paperback)

Review by André Heck
CAN/Amstel Institute
University of Amsterdam, The Netherlands

Animating Calculus is a collection of 22 Mathematica labs to explore calculus and visualize concepts through computation and animation. It can be used for self-study, demonstration, or as a laboratory supplement to a first year calculus course. Each lab can be used independent of the others; the prerequisites and required Mathematica techniques are summarized in the lab overview at the beginning.

The first two labs introduce the reader in a concise way to the basics of Mathematica. Two appendices support the usage of the computer algebra system and the procedures especially written for ``Animating Calculus.'' The other labs are all about calculus and consist mostly of exercises. No output of Mathematica commands is displayed in the book and no answers to the exercises are provide. So, the reader is supposed to work through the notebooks behind computer. As the title of the book suggests, visualization of concepts plays a major role in these labs. Samples from notebooks can be found on http// They give a good idea of the broad range of calculus topics treated. derivatives and rate of change, extrema, limits, symbolic and numerical integration, differential equations and Euler's method, and series approximations are more or less standard. But, population dynamics and iteration, harmonic series, modeling of landing an airplane, the Buffon needle problem, and tracing rolling wheels are unusual topics. The exercises and examples in the labs are well-chosen: they are attractive, relevant for most calculus course, at the right student-level, and they stimulate the use of computer algebra technology while studying mathematics.

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