Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition: (Textbooks in Mathematics)

The Second Edition combines a traditional approach with the symbolic manipulation abilities of Mathematica to explain and develop the classical theory of curves and surfaces. You will learn to reproduce and study interesting curves and surfaces - many more than are included in typical texts - using computer methods. By plotting geometric objects and studying the printed result, teachers and students can understand concepts geometrically and see the effect of changes in parameters. Modern Differential Geometry of Curves and Surfaces with Mathematica explains how to define and compute standard geometric functions, for example the curvature of curves, and presents a dialect of Mathematica for constructing new curves and surfaces from old. The book also explores how to apply techniques from analysis. Although the book makes extensive use of Mathematica, readers without access to that program can perform the calculations in the text by hand. While single- and multi-variable calculus, some linear algebra, and a few concepts of point set topology are needed to understand the theory, no computer or Mathematica skills are required to understand the concepts presented in the text. In fact, it serves as an excellent introduction to Mathematica, and includes fully documented programs written for use with Mathematica. Ideal for both classroom use and self-study, Modern Differential Geometry of Curves and Surfaces with Mathematica has been tested extensively in the classroom and used in professional short courses throughout the world.

Table of Contents:
Curves in the Plane Studying Curves in the Plane with Mathematica Famous Plane Curves Alternate Methods for Plotting Plane Curves New Curves from Old Determining a Plane Curve from Its Curvature Global Properties of Plane Curves Curves in Space Tubes and Knots Construction of Space Curves Calculus on Euclidean Space Surfaces in Euclidean Space Examples of Surfaces Nonorientable Surfaces Metrics on Surfaces Surfaces in 3-Dimensional Space Surfaces in 3-Dimensional Space via Mathematica Asymptotic Curves on Surfaces Ruled Surfaces Surfaces of Revolution Surfaces of Constant Gaussian Curvature Intrinsic Surface Geometry Differentiable Manifolds Riemannian Manifolds Abstract Surfaces Geodesics on Surfaces The Gauss-Bonnet Theorem Principal Curves and Umbilic Points Triply Orthogonal Systems of Surfaces Minimal Surfaces Minimal Surfaces and Complex Variables Minimal Surfaces via the Weierstrass Representation Minimal Surfaces via Bjorling's Formula Construction of Surfaces Canal Surfaces and Cyclides of Dupin Inversions of Curves and Surfaces Appendices General Programs Curves Surfaces Plotting Programs Bibliography Index Name Index Miniprogram and Mathematica Command Index

About the Author :
Gray; Alfred University of Maryland, College Park, USA,

Review :
"I wish that I would have used this book as my introduction to differential geometry instead of the here-unnamed horror-flick-of-a-book required by my early professors on the subjectIn the high-turnover of textbooks this much improved 2nd edition is truly deserving of the title and furthermore acts as an excellent tribute to its author." - The Mathematica Journal, Vol. 7 No. 2, 1998 "More than any other text I am aware of, Gray integrates computing into the materialGray's Mathematica programs offer new and fascinating ways to present material. With an appropriate selection of material the first edition and, even better, the present second edition, may provide an excellent background for a course on the subjectsecond edition provides considerable extensions of the subjectsauthor's acknowledgements show that comments from a lot of well-known geometers have lead to an improvement of the book." --Bernd Wegner, Zentralblatt MATH, Vol. 942