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.
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Book Description
Editorial Reviews
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"This delightfully written book overflows with beautiful mathematics, requiring only linear algebra, multi-variable calculus, and a little mathematical sophistication." The American Mathematical Monthly
Book Description
The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. The authors take a novel approach in this revised edition of a successful textbook by casting the theory into a new light, that of singularity theory.
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Most Helpful Customer Reviews
5 of 7 people found the following review helpful:
5.0 out of 5 stars
Curves and Singularities is a Fascinating Book,
By Michael Morelli (Lumberton, NJ) - See all my reviews
This review is from: Curves and Singularities: A Geometrical Introduction to Singularity Theory (Paperback)
The book "Curves and Singularities" is an excellent introduction to the the use of calculus in studying curves and surfaces. I enjoyed the sections on osculating cirles, degree of contace, envelopes, and jets. There are many exercies and examples to guide the reader.
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Inside This Book
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First Sentence:
Plane curves arise naturally in all sorts of situations and in many guises. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
unit speed plane curve, ordinary inflexions, higher inflexions, midpoint locus, rhamphoid cusp, transversality lemma, versal unfolding, parametrized manifolds, bitangent circles, higher vertices, smooth germ, ordinary vertex, ordinary cusp, inflexional tangent, catastrophe machine, apparent contour, cuspidal edge, discriminant set, pedal curve, tangent developable, regular value, bifurcation set, right equivalence, local diffeomorphism, dual curve Key Phrases - Capitalized Phrases (CAPs): (learn more)
Definition Let, Proposition Let, Proof Let, Proof Write New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Plane curves arise naturally in all sorts of situations and in many guises. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
unit speed plane curve, ordinary inflexions, higher inflexions, midpoint locus, rhamphoid cusp, transversality lemma, versal unfolding, parametrized manifolds, bitangent circles, higher vertices, smooth germ, ordinary vertex, ordinary cusp, inflexional tangent, catastrophe machine, apparent contour, cuspidal edge, discriminant set, pedal curve, tangent developable, regular value, bifurcation set, right equivalence, local diffeomorphism, dual curve Key Phrases - Capitalized Phrases (CAPs): (learn more)
Definition Let, Proposition Let, Proof Let, Proof Write New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
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29
books
cite this book:
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- Differential Topology by Victor Guillemin in Back Matter
- Differentiable Germs and Catastrophes (London Mathematical Society Lecture Note Series) by Theodor Bröcker in Back Matter
- Differential Equations (2nd Edition) by John Polking in Back Matter
- Microcomputers and Mathematics by James William Bruce in Back Matter
- Catastrophe Theory by Vladimir I. Arnol'd in Back Matter
See all 27 books this book cites
- Transform Methods in Applied Mathematics: An Introduction (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Peter Lancaster on page 213, and Back Matter
- Microcomputers and Mathematics by James William Bruce on page 139, and page 244
- Computer-Aided Analysis of Difference Schemes for Partial Differential Equations by Victor G. Ganzha on page 196, and page 237
- Computer Vision - ECCV 2000: 6th European Conference on Computer Vision Dublin, Ireland, June 26 - July 1, 2000 Proceedings, Part I (Lecture Notes in Computer Science) by David Vernon on page 751, and page 797
- Introduction to Implicit Surfaces (The Morgan Kaufmann Series in Computer Graphics) by Jules Bloomenthal in Back Matter (1), and Back Matter (2)
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