Curves and singularities : a geometrical introduction to singularity theory

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Curves and singularities : a geometrical introduction to singularity theory / J.W. Bruce, P.J. Giblin

版:

2nd ed

資料種別:

図書

出版情報:

New York : Cambridge University Press, 1992

形態:

xviii, 321 p. ; 23 cm

著者名:

ISBN:

9780521419857 [0521419859] (: hardback)
9780521429993 [0521429994] (: paperback)

書誌ID:

BA18911588

子書誌情報

フルテキスト

所蔵情報

他の版・巻

Curves and singularities : a geometrical introduction to singularity theory (: hard ; : pbk)
J.W. Bruce and P.J. Giblin , Cambridge University Press , 1984

書誌詳細

注記:

Includes further reading (p. 305), bibliographical references (p. 306-308), index of notation, and index

主題:

Curves; Singularities (Mathematics)

言語:

英語

目次情報:

Preface to the second edition

Preface to the first edition

Introductory example: a gravitational catastrophe machine / 1：

Curves, and functions on them / 2：

Parametrized curves

Tangent vectors

Contact

Reparametrization

Curvature

Functions on plane curves

Space curves

More about functions / 3：

Right equivalence

Flat functions

Jets

Regular values and smooth manifolds / 4：

Smooth maps and parametrized manifolds

Regular values

Tangent spaces

The Morse lemma

Morse lemma with parameters

Envelopes / 5：

Families and envelopes

Other definitions of envelope

Local structure of envelopes

Examples of envelopes

Envelopes and differential equations

Unfoldings / 6：

Unfoldings and (p)versal unfoldings

Versal unfoldings

Cusps

Unfoldings: applications / 7：

Distance-squared and height functions

Developable surfaces and the tangent developable of a space curve

Some different local pictures

Symmetry sets

Caustics by reflexion

Duals and differential equations

Transversality / 8：

Smooth manifolds

Thom's transversality lemma

Algebraic surfaces and more on apparent contours

Open and dense properties

Generic properties of curves / 9：

The Monge-Taylor map

A transversality theorem for space curves

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