Differential Geometry of Curves and Surfaces

ISBN-13: 9781482247343 / Angielski / Twarda / 2015 / 414 str.

Thomas F. Banchoff; Stephen T. Lovett

Opis

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."

Spis treści

Plane Curves: Local Properties. Plane Curves: Global Properties. Curves in Space: Local Properties. Curves in Space: Global Properties. Regular Surfaces. The First and Second Fundamental Forms. The Fundamental Equations of Surfaces. The Gauss–Bonnet Theorem and Geometry of Geodesics. Curves and Surfaces in n-Dimensional Euclidean Space. Appendix.