Curves and Singularities
A Geometrical Introduction to Singularity Theory

This second edition is an invaluable textbook for anyone who would like an introduction to the modern theories of catastrophies and singularities.

J. W. Bruce (Author), P. J. Giblin (Author)

9780521419857, Cambridge University Press

Hardback, published 26 November 1992

340 pages
23.8 x 15.9 x 2.5 cm, 0.656 kg

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

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which 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 modern singularity theory.

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.

Subject Areas: Geometry [PBM]