Differential geometry of curves and surfaces
 Responsibility
 Thomas Banchoff, Stephen Lovett.
 Edition
 Second edition.
 Publication
 Boca Raton : CRC Press, Taylor & Francis Group, 2015.
 Copyright notice
 ©2016
 Physical description
 xvi, 414 pages : illustrations, charts ; 25 cm
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA641 .B32 2015  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Banchoff, Thomas, author.
 Contributor
 Lovett, Stephen (Stephen T.)
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 405407) and index.
 Contents

 Plane Curves: Local Properties Parametrizations Position, Velocity, and Acceleration Curvature Osculating Circles, Evolutes, and Involutes Natural Equations
 Plane Curves: Global Properties Basic Properties Rotation Index Isoperimetric Inequality Curvature, Convexity, and the FourVertex Theorem
 Curves in Space: Local Properties Definitions, Examples, and Differentiation Curvature, Torsion, and the Frenet Frame Osculating Plane and Osculating Sphere Natural Equations
 Curves in Space: Global Properties Basic Properties Indicatrices and Total Curvature Knots and Links
 Regular Surfaces Parametrized Surfaces Tangent Planes and Regular Surfaces Change of Coordinates The Tangent Space and the Normal Vector Orientable Surfaces
 The First and Second Fundamental Forms The First Fundamental Form Map Projections (Optional) The Gauss Map The Second Fundamental Form Normal and Principal Curvatures Gaussian and Mean Curvature Developable Surfaces and Minimal Surfaces
 The Fundamental Equations of Surfaces Gauss's Equations and the Christoffel Symbols Codazzi Equations and the Theorema Egregium The Fundamental Theorem of Surface Theory
 The GaussBonnet Theorem and Geometry of Geodesics Curvatures and Torsion GaussBonnet Theorem, Local Form GaussBonnet Theorem, Global Form Geodesics Geodesic Coordinates Applications to Plane, Spherical and Elliptic Geometry Hyperbolic Geometry
 Curves and Surfaces in nDimensional Euclidean Space Curves in nDimensional Euclidean Space Surfaces in Rn
 Appendix: Tensor Notation.
 (source: Nielsen Book Data)
 Summary

Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students' geometric intuition through interactive computer graphics applets supported by sound theory. The book explains the reasons for various definitions while the interactive applets offer motivation for certain definitions, allow students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. New to the Second Edition * Reworked presentation to make it more approachable * More exercises, both introductory and advanced * New section on the application of differential geometry to cartography * Additional investigative project ideas * Significantly reorganized material on the GaussBonnet theorem * Two new sections dedicated to hyperbolic and spherical geometry as applications of intrinsic geometry * A new chapter on curves and surfaces in Rn Suitable for an undergraduatelevel course or selfstudy, this selfcontained textbook and online software applets provide students with a rigorous yet intuitive introduction to the field of differential geometry. The text gives a detailed introduction of definitions, theorems, and proofs and includes many types of exercises appropriate for daily or weekly assignments. The applets can be used for computer labs, inclass illustrations, exploratory exercises, or selfstudy aids.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2015
 Copyright date
 2016
 Note
 "A Chapman & Hall book."
 ISBN
 9781482247343 (hbk : alk. paper)
 1482247348 (hbk : alk. paper)