Geometric differentiation : for the intelligence of curves and surfaces

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Geometric differentiation : for the intelligence of curves and surfaces / I.R. Porteous

版:: 2nd ed
資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, c2001
形態:: xv, 333 p. ; 24 cm
著者名:: Porteous, Ian R <DA06616430>
ISBN:: 9780521810401 [052181040X]
9780521002646 [0521002648] (: pbk.)
書誌ID:: BA5497820X

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Geometric differentiation : for the intelligence of curves and surfaces
I.R. Porteous , Cambridge University Press , 1994

書誌詳細

注記:

Includes bibliographical references and index

主題:

Curves; Geometry, Differential; Surfaces

言語:

英語

目次情報:

Introduction

Plane curves / 1：

Regular plane curves and their evolutes / 1.0：

Curvature / 1.2：

Parallels / 1.3：

Equivalent parametric curves / 1.4：

Unit-speed curves / 1.5：

Unit-angular-velocity curves / 1.6：

Rhamphoid cusps / 1.7：

The determination of circular points / 1.8：

The four-vertex theorem / 1.9：

Exercises

Some elementary geometry / 2：

Some linear facts / 2.0：

Some bilinear facts / 2.2：

Some projective facts / 2.3：

Projective curves / 2.4：

Spaces of polynomials / 2.5：

Inversion and stereographic projection / 2.6：

Plane kinematics / 3：

Instantaneous rotations and translations / 3.0：

The motion of a plane at t = 0 / 3.2：

The inflection circle and Ball point / 3.3：

The cubic of stationary curvature / 3.4：

Burmester points / 3.5：

Rolling wheels / 3.6：

Polodes / 3.7：

Caustics / 3.8：

The derivatives of a map / 4：

The first derivative and C[superscript 1] submanifolds / 4.0：

Higher derivatives and C[superscript k] submanifolds / 4.2：

The Faa de Bruno formula / 4.3：

Curves on the unit sphere / 5：

Geodesic curvature / 5.0：

Spherical kinematics / 5.2：

Space curves / 6：

The focal surface and space evolute / 6.0：

The Serret--Frenet equations / 6.3：

Close up views / 6.4：

Historical note / 6.6：

k-times linear forms / 7：

Quadratic forms on R[superscript 2] / 7.0：

Cubic forms on R[superscript 2] / 7.3：

Use of complex numbers / 7.4：

Probes / 8：

Probes of smooth map-germs / 8.0：

Probing a map-germ V: R[superscript 2]--R / 8.2：

Optional reading / 8.3：

Contact / 9：

Contact equivalence / 9.0：

K-equivalence / 9.2：

Applications / 9.3：

Surfaces in R[superscript 3] / 10：

Euler's formula / 10.0：

The sophisticated approach / 10.2：

Lines of curvature / 10.3：

Focal curves of curvature / 10.4：

Ridges and ribs / 10.5：

The normal bundle of a surface / 11.0：

Isolated umbilics / 11.2：

The normal focal surface / 11.3：

A classification of focal points / 11.4：

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