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

Email: `heck@can.nl`

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//www.teloscom.pub/catalog/MATHEMATICS/AnimCalc.html`

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.