Geometric Differentiation

Ian R. Porteous

334 pages, parution le 15/03/2002 (2^eme édition)

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Résumé

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 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.

Contents

Introduction

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.

Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Ian R. Porteous
Parution	15/03/2002
Édition	2^eme édition
Nb. de pages	334
Format	15 x 23
Couverture	Broché
Poids	596g
Intérieur	Noir et Blanc
EAN13	9780521002646
ISBN13	978-0-521-00264-6