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Look Inside Geometric Differentiation

Geometric Differentiation
For the Intelligence of Curves and Surfaces

2nd Edition

£126.00

  • Date Published: December 2001
  • availability: Available
  • format: Hardback
  • isbn: 9780521810401

£ 126.00
Hardback

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Description
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About the Authors
  • 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
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    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

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    Product details

    • Edition: 2nd Edition
    • Date Published: December 2001
    • format: Hardback
    • isbn: 9780521810401
    • length: 350 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.64kg
    • contains: 39 b/w illus. 26 colour illus.
    • availability: 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.

  • Author

    I. R. Porteous, University of Liverpool

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