Vector calculus. linear algebra and differential forms - 3rd Edition：向量微积分、线性代数和微分形式

图书标准信息

• 作者 [美]哈伯德（Hubbard J.H.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 3
• ISBN 9787510061509
• 定价 169.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 802页
• 正文语种 英语

【内容简介】

　　《数学经典教材：向量微积分、线性代数和微分形式（第3版）（影印版）》是一部优秀的微积分教材，好评不断。《数学经典教材：向量微积分、线性代数和微分形式（第3版）（影印版）》材料的选择和编排有不同于标准方法的三点：（一）在这个水平的研究中，线性代数是研究多变量微积分的极其方便的环境和语言，非线性更像是一个衍生产品；（二）强调计算有效算法，并且通过这些算术工作来证明定理；（三）运用微分形式推广更高维的积分定理。
　　目次：预备知识；向量、矩阵和导数；解方程；流形、泰勒多项式和二次型、曲率；积分；流形的体积；形式和向量微积分。附录：分析。
　　《数学经典教材：向量微积分、线性代数和微分形式（第3版）（影印版）》读者对象：数学专业的本科生以及想学习微积分知识的广大非专业专业人士。

【作者简介】

John Hamal Hubbard was born on October 6 or 7, 1945 (the actual date is unknown). He is an American mathematician who is currently a professor at Cornell University and the Université de Provence. He is well known for the mathematical contributions he made with Adrien Douady in the field of complex dynamics, including a study of the Mandelbrot set. One of their most important results is that the Mandelbrot set is connected.Hubbard graduated with a Doctorat d'État from Université de Paris-Sud in 1973 under the direction of Adrien Douady; his thesis was entitled Sur Les Sections Analytiques de La Courbe Universelle de Teichmüller and was published by the American Mathematical Society.

【目录】

Preface

Chapter0preliminaries
0.0introduction
0.1readingmathematics
0.2quantifiersandnegation
0.3settheory
0.4functions
0.5realnumbers
0.6infinitesets
0.7complexnumbers

Chapter1vectors～matrices,andderivatives
1.0introduction
1.1introducingtheactors:pointsandvectors
1.2introducingtheactors:matrices
1.3matrixmultiplicationasalineartransformation
1.4thegeometryofrn
1.5limitsandcontinuity
1.6fourbigtheorems
1.7derivativesinseveralvariablesaslineartransformations
1.8rulesforcomputingderivatives
1.9themeanvaluetheoremandcriteriafordifferentiability
1.10reviewexercisesforChapter1

Chapter2solvingequations
2.0introduction
2.1themainalgorithm:rowreduction
2.2solvingequationswithrowreduction
2.3matrixinversesandelementarymatrices
2.4linearcombinations,span,andlinearindependence
2.5kernels,images,andthedimensionformula
2.6abstractvectorspaces
2.7eigenvectorsandeigenvalues
2.8newton'smethod
2.9superconvergence
2.10theinverseandimplicitfunctiontheorems
2.11reviewexercisesforChapter2

Chapter3manifolds,Taylorpolynomials,quadraticforms,andcurvature
3.0introduction
3.1manifolds
3.2tangentspaces
3.3Taylorpolynomialsinseveralvariables
3.4rulesforcomputingTaylorpolynomials
3.5quadraticforms
3.6classifyingcriticalpointsoffimctions
3.7constrainedcriticalpointsandlagrangemultipliers
3.8geometryofcurvesandsurfaces
3.9reviewexercisesforChapter3

Chapter4integration
4.0introduction
4.1definingtheintegral
4.2probabilityandcentersofgravity
4.3whatfunctionscanbeintegrated?
4.4measurezero
4.5fhbini'stheoremanditeratedintegrals
4.6numericalmethodsofintegration
4.7otherpavings
4.8determinants
4.9volumesanddeterminants
4.10thechangeofvariablesformula
4.11lebesgueintegrals
4.12reviewexercisesforChapter4

Chapter5volumesofmanifolds
5.0introduction
5.1parallelogramsandtheirvolumes
5.2parametrizations
5.3computingvolumesofmanifolds
5.4integrationandcurvature
5.5fractalsandfractionaldimension
5.6reviewexercisesforChapter5

Chapter6formsandvectorcalculus
6.0introduction
6.1formsonrn
6.2integratingformfieldsoverparametrizeddomains
6.3orientationofmanifolds
6.4integratingformsoverorientedmanifolds
6.5formsinthelanguageofvectorcalculus
6.6boundaryorientation
6.7theexteriorderivative
6.8grad,curl,div,andallthat
6.9electromagnetism
6.10thegeneralizedstokes'stheorem
6.11theintegraltheoremsofvectorcalculus
6.12potentials
6.13reviewexercisesforChapter6

Appendix:analysis
A.0introduction
A.1arithmeticofrealnumbers
A.2cubicandquarticequations
A.3tworesultsintopology:nestedcompactsetsandheine-borel
A.4proofofthechainrule
A.5proofofkantorovich'stheorem
A.6proofoflemma2.9.5（superconvergence）
A.7proofofdifferentiabilityoftheinversefunction
A.8proofoftheimplicitfunctiontheorem
A.9provingequalityofcrossedpartials
A.10functionswithmanyvanishingpartialderivatives
A.11provingrulesforTaylorpolynomials;bigoandlittleo
A.12Taylor'stheoremwithremainder
A.13provingtheorem3.5.3（completingsquares）
A.14geometryofcurvesandsurfaces:proofs
A.15Stirling'sformulaandproofofthecentrallimittheorem
A.16provingfubiul'stheorem
A.17justifyingtheuseofotherpavings
A.18resultsconcerningthedeterminant
A.19changeofvariablesformula:arigorousproof
A.20justifyingvolume0
A.21lebesguemeasureandproofsforlebesgueintegrals
A.22justifyingthechangeofparametrization
A.23computingtheexteriorderivative
A.24thepullback
A.25provingstokes'stheorem

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