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Geometric differentiation : for the intelligence of curves and surfaces

Author: Ian R Porteous
Publisher: Cambridge : Cambridge University Press, 2001.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
Inspired by the work of Thom and Arnol'd on singularity theory, such topics as umbilics, ridges and subparabolic lines, which are rarely treated in elementary courses on differential geometry, are considered in this volume.
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Document Type: Book
All Authors / Contributors: Ian R Porteous
ISBN: 9780521002646 0521002648 9780521810401 052181040X
OCLC Number: 1055936849
Notes: Previous ed.: 1994.
Target Audience: Specialized.
Description: 350p. ; 23 cm.
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.
Responsibility: I.R. Porteous.

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This is a revised and up-dated version of the popular first edition. The topics covered here are of immediate relevance to many modern applications. As such this text will appeal to scientists and  Read more...

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'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 Read more...

 
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