Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition

Alfred Gray

ISBN 10: 0849371643 / ISBN 13: 9780849371646

Editore: CRC-Press, 1997

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Riassunto:

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.

Contenuti: 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

Dati bibliografici

Titolo: Modern Differential Geometry of Curves and ...
Casa editrice: CRC-Press
Data di pubblicazione: 1997
Legatura: Hardcover
Condizione: Good
Edizione: seconda edizione