Curves and singularities : a geometrical introduction to singularity theory

所蔵情報QRコード

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

資料種別:

図書

出版情報:

Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984

形態:

xii, 222 p. ; 24 cm

著者名:

ISBN:

9780521249454 [0521249457] (: hard)
9780521270915 [052127091X] (: pbk)

書誌ID:

BA03120942

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. 2nd ed (: hardback ; : paperback)
J.W. Bruce, P.J. Giblin , Cambridge University Press , 1992

書誌詳細

注記:

Includes bibliographies and indexes

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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