微分几何中的初等论题9787510058363

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作者(美)索普

出版社世界图书出版公司

ISBN9787510058363

出版时间2013-03

装帧其他

开本其他

定价49元

货号2597068

上书时间2024-07-27

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商品描述: 导语摘要
《微分几何中的初等论题》由J.A.Thorpe（索普）著，主要内容：Thisbookdevelopsthegeometryofn-dimensionalsurfacesin(n+1)．space．ItiSdesignedforal-semesterdifrorentialgeometrycourseatthejunior-seniorIevel．Itdrawssignificantlyonthecontemporarystudent'sknowledgeoflinearalgebra，multivariatecalculus，anddifferentialequations．therebysolidifyingthestudent’SunderstandingoftheseSUbjects．Indeed．oneofthereasonsthatacourseindifierentialgeometryiSSOvaluableatthislevelisthatitdoesturnoutstudentswithathoroughunderstandingofseveralvariablecalcuills.

目录
Chapter 1
Graphs and Level Sets
Chapter 2
Vector Fields
Chapter 3
The Tangent Space
Chapter 4
Surfaces
Chapter 5
Vector Fields on Surfaces; Orientation
Chapter 6
The Gauss Map
Chapter 7
Geodesics
Chapter 8
Parallel Transport
Chapter 9
The Weingarten Map
Chapter 10
Curvature of Plane Curves
Chapter l 1
Arc Length and Line Integrals
Chapter 12
Curvature of Surfaces
Chapter 13
Convex Surfaces
Chapter 14
Parametrized Surfaces
Chapter 15
Local Equivalence of Surfaces and Parametrized
Surfaces
Chapter 16
Focal Points
Chapter 17
Surface Area and Volume
Chapter 18
Minimal Surfaces
Chapter 19
The Exponential Map
Chapter 20
Surfaces with Boundary
Chapter 21
The Gauss-Bonnet Theorem
Chapter 22
Rigid Motions and Congruence
Chapter 23
Isometries
Chapter 24
Riemannian Metrics
Bibliography
Notational Index
Subject Index

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