Geometric differentiation : for the intelligence of curves and surfaces

著者

• Porteous, Ian R

書誌事項

Geometric differentiation : for the intelligence of curves and surfaces

I.R. Porteous

Cambridge University Press, c2001

2nd ed

• : pbk.

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA5497820X
• ISBN:
  • 9780521810401
  • 9780521002646
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xv, 333 p.
• 大きさ: 24 cm
• 件名:
  • LCSH : Geometry, Differential
  • LCSH : Curves
  • LCSH : Surfaces