经典数学丛书（影印版）：多元微积分教程

图书标准信息

• 作者 [印]戈培德（Ghorpade S.R.） 著
• 出版社 世界图书出版公司
• 出版时间 2014-05
• 版次 1
• ISBN 9787510075926
• 定价 79.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 475页
• 正文语种 英语
• 丛书 经典数学丛书

【内容简介】

　　Calculusofreal-valuedfunctionsofseveralrealvariables，alsoknownasmultivariablecalculus，isarichandfascinatingsubject.Ontheonehand，itseekstoextendeminentlyusefulandimmenselysuccessfulnotionsinone-variablecalculussuchaslimit，continLuty，derivative，andintegralto"higherdimensions."Ontheotherhand，thefactthatthereismuchmoreroomtomoveaboutinthe'nspaceRnthanonthereallineRbringstotheforedeepergeometricandtopologicalnotionsthatplayasignificantroleinthestudyoffunctionsoftwoormorevariables.

【目录】

1VectorsandFunctions
1.1Preliminaries
AlgebraicOperations
OrderProperties
Intervals,Disks,andBoundedSets
LineSegmentsandPaths
1.2FunctionsandTheirGeometricProperties
BasicNotions
BoundedFunctions
MonotonicityandBimonotonicity
FunctionsofBoundedVariation
FunctionsofBoundedBivariation
ConvexityandConcavity
LocalExtremaandSaddlePoints
IntermediateValueProperty
1.3CylindricajandSphericalCoordinates
CylindricalCoordinates
SphericalCoordinates
NotesandComments
Exercises

2Sequences,Continuity,andLimits
2.1SequencesinR2
,SubsequencesandCauchySequences
Closure,Boundary,andInterior
2.2Continuity
CompositionofContinuousFunctions
PiecingContinuousFunctionsonOverlappingSubsets
CharacterizationsofContinuity
ContinuityandBoundedness
ContinuityandMonotonicity
Continuity,BoundedVariation,andBoundedBivariation
ContinuityandConvexity
ContinuityandIntermediateValueProperty
UniformContinuity
ImplicitFunctionTheorem
2.3Limits
LimitsandContinuity
LimitfromaQuadrant
ApproachingInfinity
NotesandComments
Exercises

3PartialandTotalDifferentiation
3.1PartialandDirectionalDerivatives
PartialDerivatives
DirectionalDerivatives
Higher-OrderPartialDerivatives
Higher-OrderDirectionalDerivatives
3.2Differentiability
DifferentiabilityandDirectionalDerivatives
ImplicitDifferentiation
3.3Taylor'sTheoremandChainRule
BivariateTaylorTheorem
ChainRule
3.4MonotonicityandConvexity
MonotonicityandFirstPartials
BimonotonicityandMixedPartials
BoundedVariationandBoundednessofFirstPartials
BoundedBivariationandBoundednessofMixedPartials
ConvexityandMonotonicityofGradient
ConvexityandNonnegativityofHessian
3.5FunctionsofThreeVariables.,
ExtensionsandAnalogues
TangentPlanesandNormalLinestoSurfaces
ConvexityandTernaryQuadraticForms
NotesandComments
Exercises

4ApplicationsofPartialDifferentiation
4.1AbsoluteExtrema
BoundaryPointsandCriticalPoints
4.2ConstrainedExtrema
LagrangeMultiplierMethod
CaseofThreeVariables
4.3LocalExtremaandSaddlePoints
……
5MultipleIntegration
6ApplicationsandApproximationsofMultipleIntegrals
7DoubleSeriesandImproperDoubleIntegrals
References
ListofSymbolsandAbbreviations
Index