Geometric Differentiation: For the Intelligence of Curves and Surfaces

ISBN-13: 9780521810401 / Angielski / Twarda / 2001 / 350 str.

Ian R. Porteous

Opis

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 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 should 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.

Recenzje

'… 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

Spis treści

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.