Curves and Singularities

A Geometrical Introduction to Singularity Theory

J. W. Bruce (University of Liverpool), P. J. Giblin (University of Liverpool)

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English

Cambridge University Press
25 January 1993

Euclidean geometry

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples.

A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory.

Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities.

The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus.

Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities.

By: J. W. Bruce (University of Liverpool), P. J. Giblin (University of Liverpool)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 238mm, Width: 159mm, Spine: 25mm
Weight: 656g
ISBN: 9780521419857
ISBN 10: 0521419859
Pages: 340
Publication Date: 25 January 1993
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

1. Introductory example: a gravitational catastrophe machine; 2. Curves, and functions on them; 3. More about functions; 4. Regular values and smooth manifolds; 5. Envelopes; 6. Unfoldings; 7. Unfoldings: applications; 8. Transversality; 9. Generic properties of curves; 10. More on unfoldings; 11. Singular points, several variables and generic surfaces; Appendix: Null sets and Sard's theorem.

Reviews for Curves and Singularities: A Geometrical Introduction to Singularity Theory

"""This delightfully written book overflows with beautiful mathematics, requiring only linear algebra, multi-variable calculus, and a little mathematical sophistication."" The American Mathematical Monthly"