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This is a revised and extended version of the popular first edition. Inspired by the work of Thom and Arnold on singularity theory, such topics as umbilics, ridges and subparabolic lines, all robust features of a smooth surface, which are rarely treated in elementary courses on differential geometry, are considered here in detail. These features are of immediate relevance in modern areas of application such as interpretation of range data from curved surfaces and the processing of magnetic resonance and cat-scan images. The author has included many exercises and examples to illustrate the results proved.Read more
- Revised and up-dated edition
- Covers many topics not covered in elementary differential geometry courses
- Many examples and exercises
Reviews & endorsements
"Porteous' approach is distinguished by the extreme richness of the examples he treats, and his novel emphasis on certain concepts--ridges, ribs, umbilics--where third-and-higher-order derivates are crucial. The book's illustrations are helpful and elegant...highly recommended." Choice
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- Edition: 2nd Edition
- Date Published: December 2001
- format: Hardback
- isbn: 9780521810401
- length: 350 pages
- dimensions: 229 x 152 x 21 mm
- weight: 0.64kg
- contains: 39 b/w illus. 26 colour illus.
- availability: Available
Table of Contents
1. Plane curves
2. Some elementary geometry
3. Plane kinetics
4. The derivatives of a map
5. Curves on the unit sphere
6. Space curves
7. k-times linear forms
10. Surfaces in R3
11. Ridges and ribs
13. The parabolic line
14. Involutes of geodesic foliations
15. The circles of a surface
16. Examples of surfaces
17. Flexicords of surfaces
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