分析中的问题与定理（第1卷）

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