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Geometric Differentiation

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Geometric Differentiation

Geometric Differentiation

For the Intelligence of Curves and Surfaces
2nd Edition
I. R. Porteous, University of Liverpool
December 2001
Available
Hardback
9780521810401
£141.00
GBP
Hardback
    Description

    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.

    • Revised and up-dated edition
    • Covers many topics not covered in elementary differential geometry courses
    • Many examples and exercises

    Reviews & endorsements

    'The very geometric point of view and many exercises induce me to recommend this book for everyone interested in differential geometry of curves and surfaces.' Internationale Mathematische Nachrichten

    '… 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

    See more reviews

    Product details

    December 2001
    Hardback
    9780521810401
    350 pages
    237 × 158 × 23 mm
    0.704kg
    39 b/w illus. 26 colour illus.
    Available

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    Contents

    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.
      • Show more

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    About the authors
      Author
    • I. R. Porteous , University of Liverpool

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