Elsa Abbena, Simon Salamon, Alfred Gray

Chapman and Hall/CRC

Published
June 21, 2006

Textbook
- 1016 Pages
- 531 B/W Illustrations

ISBN 9781584884484 - CAT# C4487

Series: Textbooks in Mathematics

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The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but *Mathematica *handles it easily, either through computations or through graphing curvature. Another part of *Mathematica* that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.

Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use *Mathematica* to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

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