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  《微积分和数学分析引论(第2卷)(第1册)(英文版)》适合于多种学科界的读者,如数学工作者、科学工作者、工程技术人员等。
  《微积分和数学分析引论(第2卷)(第1册)(英文版)》为全英文版。

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  《微积分和数学分析引论(第2卷)(第1册)(英文版)》在内容以及形式上有如下三个特点:一是引领读者直达本学科的核心内容;二是注重应用,指导读者灵活运用所掌握的知识;三是突出了直觉思维在数学学习中的作用。作者不掩饰难点以使得该学科貌似简单,而是通过揭示概念之间的内在联系和直观背景努力帮助那些对这门学科真正感兴趣的读者。
  《微积分和数学分析引论(第2卷)(第1册)(英文版)》各章均提供了大量的例题和习题,其中一部分有相当的难度,但绝大部分是对内容的补充。另外,《微积分和数学分析引论(第2卷)(第1册)(英文版)》附有一本专门的习题册,并且给出了习题的提示与解答。

目录

Chapter1FunctionsofSeveralVariablesandTheirDerivatives
1.1PointsandPointsSetsinthePlaneandinSpace
a.Sequencesofpoints.Convergence
b.Setsofpointsintheplane
c.Theboundaryofaset.Closedandopensets
d.Closureassetoflimitpoints
e.Pointsandsetsofpointsinspace
1.2FunctionsofSeveralIndependentVariables
a.Functionsandtheirdomains
b.Thesimplesttypesoffunctions
c.Geometricalrepresentationoffunctions
1.3Continuity
a.Definition
b.Theconceptoflimitofafunctionofseveralvariables
c.Theordertowhichafunctionvanishes
1.4ThePartialDerivativesofaFunction
a.Definition.Geometricalrepresentation
b.Examples
c.Continuityandtheexistenceofpartialderivatives
d.Changeoftheorderofdifferentiation,36
1.5TheDifferentialofaFunctionandItsGeometricalMeaning
a.Theconceptofdifferentiability
b.Directionalderivatives
c.Geometricinterpretationofdifferentiability,Thetangentplane
d.Thetotaldifferentialofafunction
e.Applicationtothecalculusoferrors
1.6FunctionsofFunctions(CompoundFunctions)andtheIntroductionofNewIndependentVariables
a.Compoundfunctions.Thechainrule
b.Examples
c.Changeofindependentvariables
1.7TheMeanValueTheoremandTaylorsTheoremforFunctionsofSeveralVariables
a.Preliminaryremarksaboutapproximationbypolynomials
b.Themeanvaluetheorem
c.Taylorstheoremforseveralindependentvariables
1.8IntegralsofaFunctionDependingonaParameter
a.Examplesanddefinitions
b.Continuityanddifferentiabilityofanintegralwithrespecttotheparameter
c.Interchangeofintegrations.Smoothingoffunctions
1.9DifferentialsandLineIntegrals
a.Lineardifferentialforms
b.Lineintegralsoflineardifferentialforms
c.Dependenceoflineintegralsonendpoints
1.10TheFundamentalTheoremonIntegrabilityofLinearDifferentialForms
a.Integrationoftotaldifferentials
b.Necessaryconditionsforlineintegralstodependonlyontheendpoints
c.Insufficiencyoftheintegrabilityconditions
d.Simplyconnectedsets
e.Thefundamentaltheorem
APPENDIX
……
Chapter2Vectors,Matrices,LinearTransformations
Chapter3DevelopmentsandApplicationsoftheDifferentialCalculus
Chapter4MultipleIntegrals
Chapter5RelationsBetweenSurfaceandVolumeIntegrals
Chapter6DifferentialEquations
Chapter7CalculusofVariations
Chapter8FunctionsofaComplexVariable
ListofBiographicalDates
Index
page543ofthisedition
page545ofthisedition

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