Geometric Differentiation
Geometric Differentiation
$187.00
USDThis is a revised and extended version of the popular first edition. Inspired by the work of Thom and Arnol'd 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 text is based on extensive teaching at Liverpool University to audiences of advanced undergraduate and beginning postgraduate students in mathematics. However, the wide applicability of this material means that it will also appeal to scientists and engineers from a variety of other disciplines. The author has included many exercises and examples to illustrate the results proved.
- 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
Product details
December 2001Hardback
9780521810401
350 pages
237 × 158 × 23 mm
0.704kg
39 b/w illus. 26 colour illus.
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
- 8. Probes
- 9. Contact
- 10. Surfaces in R3
- 11. Ridges and ribs
- 12. Umbilics
- 13. The parabolic line
- 14. Involutes of geodesic foliations
- 15. The circles of a surface
- 16. Examples of surfaces
- 17. Flexicords of surfaces
- 18. Duality.
