分析中的問(wèn)題與定理（第1卷）

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作　者：	（）George Polya，（）Gabor Szego著
出版社：	世界圖書(shū)出版北京公司
叢編項(xiàng)：	Classics in Mathematics
標(biāo)　簽：	微積分

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ISBN：	9787506266130	出版時(shí)間：	2004-01-01	包裝：	膠版紙
開(kāi)本：	22cm	頁(yè)數(shù)：	389頁(yè)	字?jǐn)?shù)：

內(nèi)容簡(jiǎn)介

　　The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes， mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter， although the mathematical fashion has greatly changed since 1024. We have restricted ours'elves to supplementing the topics originally chosen.此書(shū)為英文版！

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圖書(shū)目錄

PartOne
InfiniteSeriesandInfiniteSequences
Chapter1
Problem
NumbersOperationswithPowerSeries
1(1--31).AdditiveNumberTheory,CombinatorialProblems,andApplications
2(31.1--43.1).BinomialCoefficientsandRelatedProblems
3(44--49).DifferentiationofPowerSeries
4(50--60).FunctionalEquationsandPowerSeries
5(60.1--60.11).GaussianBinomialCoefficients
6(61--64.2).MajorantSeries
Chapter2
LinearTransformationsofSeries.ATheoremofCesaro
1(65--78).TriangularTransformationsofSequencesintoSequences
2(79--82).MoreGeneralTransformationsofSequencesintoSequences
3(83--97).TransformationsofSequencesintoFunctions.TheoremofCesaro
Chapter3
TheStructureofRealSequencesandSeries
1(98--112).TheStructureofInfiniteSequences
2(113--116).ConvergenceExponent
3(117--123).TheMaximumTermofaPowerSeries
4(124--132).Subseries
5(132.1--137).RearrangementoftheTerms
6(138--139).DistributionoftheSignsoftheTerms
Chapter4
MiscellaneousProblems
1(140--155).EnvelopingSeries
2(156--185.2).VariousPropositionsonRealSeriesandSequences
3(186--210).PartitionsofSets,CyclesinPermutations
PartTwo
Integration
Chapter1
Problem
NumbersTheIntegralastheLimitofaSumofRectangles
1(1--7).TheLowerandtheUpperSum
2(8--19.2).TheDegreeofApproximation
3(20--29).ImproperIntegralsBetweenFiniteLimits
4(30--40).ImproperIntegralsBetweenInfiniteLimits
5(41--47).ApplicationstoNumberTheory
6(48--59).MeanValuesandLimitsofProducts
7(60--68).MultipleIntegrals
Chapter2
Inequalities
1(69--94).Inequalities
2(94.1--97).SomeApplicationsofInequalities
Chapter3
SomePropertiesofRealFunctions
1(98--111).ProperIntegrals
2(112--118.1).ImproperIntegrals
3(119--127).Continuous,Differentiable,ConvexFunctions
4(128--146).SingularIntegrals.Weierstrass'Approximation
Theorem
Chapter4
VariousTypesofEquidistribution
1(147--161).CountingFunction.RegularSequences
2(162--165).CriteriaofEquidistribution
3(166--173).MultiplesofanIrrationalNumber
4(174--184).DistributionoftheDigitsinaTableofLogarithmsandRelatedQuestions
5(185--194).OtherTypesofEquidistribution
Chapter5
FunctionsofLargeNumbers
1(195--209).Laplace'sMethod
2(210--217.1).ModificationsoftheMethod
3(218--222).AsymptoticEvaluationofSomeMaxima
4(223--226).MinimaxandMaximin
PartThree
FunctionsofOneComplexVariable.GeneralPart
Chapter1
ComplexNumbersandNumberSequences
1(1--15).RegionsandCurves.WorkingwithComplexVariables
2(16--27).LocationoftheRootsofAlgebraicEquationsProblemNumbers
3(28--35).ZerosofPolynomials,Continued.ATheoremofGauss
4(36--43).SequencesofComplexNumbers
5(44--50).SequencesofComplexNumbers,Continued:TransformationofSequences
6(51--54).RearrangementofInfiniteSeries
Chapter2
MappingsandVectorFields
1(55--59).TheCauchy-RiemannDifferentialEquations
2(60--84).SomeParticularElementaryMappings
3(85--102).VectorFields
Chapter3
SomeGeometricalAspectsoiComplexVariables
1(103--116).MappingsoftheCircle.CurvatureandSupportFunction
2(117--123).MeanValuesAlongaCircle
3(124--129).MappingsoftheDisk.Area
4(130--144).TheModularGraph.TheMaximumPrinciple
Chapter4
Cauchy'sTheorem·TheArgumentPrinciple
1(145--171).Cauchy'sFormula
2(172--178).Poisson'sandJensen'sFormulas
3(179--193).TheArgumentPrinciple
4(194--206.2).Rouche'sTheorem
Chapter5
SequencesofAnalyticFunctions
1(207--229).Lagrange'sSeries.Applications
2(230--240).TheRealPartofaPowerSeries
3(241--247).PolesontheCircleofConvergence
4(248--250).IdenticallyVanishingPowerSeries
5(251--258).PropagationofConvergence
6(259--262).ConvergenceinSeparatedRegions
7(263--265).TheOrderofGrowthofCertainSequencesofPolynomials
Chapter6
TheMaximumPrinciple
1(266--279).TheMaximumPrincipleofAnalyticFunctions
2(280--298).Schwarz'sLemma
3(299--310).Hadamard'sThreeCircleTheorem
4(311--321).HarmonicFunctions
5(322--340).ThePhragmen-LindelofMethod
AuthorIndex
SubjectIndex