Geometric Differentiation
For the Intelligence of Curves and Surfaces

This is a revised version of the popular Geometric Differentiation, first edition.

I. R. Porteous (Author)

9780521810401, Cambridge University Press

Hardback, published 13 December 2001

350 pages, 39 b/w illus. 26 colour illus.
23.7 x 15.8 x 2.3 cm, 0.704 kg

'… a very good and interesting introduction to differential geometry of curves and surfaces, which can be recommended to anybody interested in the subject.' EMS Newsletter

This 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.

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.

Subject Areas: Topology [PBP], Geometry [PBM]