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Differential Geometry of Curves and Surfaces (Revised) (Hardcover) (Thomas Banchoff & Stephen Lovett)
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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.
Differential Geometry of Curves and Surfaces, Second Edition studies properties of geometric objects using the tools learned in calculus and linear algebra. It solidifies the techniques of multivariable calculus since the big theorem in the subject, the Gauss-Bonnet Theorem, and makes use of so many of the topics that might appear disconnected in the calculus sequence. In addition to clear exposition and comprehensive exercises, the book is accompanied online interactive Java applets coordinated with each section.