Differential geometry of curves and surfaces
- Thomas Banchoff, Stephen Lovett.
- Second edition.
- Boca Raton : CRC Press, Taylor & Francis Group, 2015.
- Copyright notice
- Physical description
- xvi, 414 pages : illustrations, charts ; 25 cm
At the library
Science Library (Li and Ma)
|QA641 .B32 2015||Unknown|
- Includes bibliographical references (pages 405-407) and index.
- 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 Four-Vertex 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 Gauss-Bonnet Theorem and Geometry of Geodesics Curvatures and Torsion Gauss-Bonnet Theorem, Local Form Gauss-Bonnet Theorem, Global Form Geodesics Geodesic Coordinates Applications to Plane, Spherical and Elliptic Geometry Hyperbolic Geometry
- Curves and Surfaces in n-Dimensional Euclidean Space Curves in n-Dimensional Euclidean Space Surfaces in Rn
- Appendix: Tensor Notation.
- (source: Nielsen Book Data)
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 Gauss-Bonnet 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 undergraduate-level course or self-study, this self-contained 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, in-class illustrations, exploratory exercises, or self-study aids.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- "A Chapman & Hall book."
- 9781482247343 (hbk : alk. paper)
- 1482247348 (hbk : alk. paper)
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