分析中的问题与定理（第2卷）

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作　者：	（）George Polya，（）Gabor Szego著
出版社：	世界图书出版北京公司
丛编项：	Classics in Mathematics
标　签：	微积分

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ISBN：	9787506266024	出版时间：	2004-01-01	包装：	胶版纸
开本：	22cm	页数：	391页	字数：

内容简介

　　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.此书为英文版！

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图书目录

PartFour.FunctionsofOneComplexVariable.SpecialPart
Chapter1.MaximumTermandCentralIndex,MaximumModulusandNumberofZeros
Problem
Numbers
1(1-40)Analogybetweenu(r)andM(r),v(r)andN(r)
2(41-47)FurtherResultsonu(r)andv(r)
3(48-66)Connectionbetweenu(r),v(r),M(r)andN(r)
4(67-76)u(r)andM(r)underSpecialRegularityAssumptions
Chapter2.SehlichtMappings
1(77-83)IntroductoryMaterial
2(84-87)UniquenessTheorems
3(88-96)ExistenceoftheMappingFunction
4(97-120)TheInnerandtheOuterRadius.TheNormedMappingFunction
5(121-135)RelationsbetweentheMappingsofDifferentDomains
6(136-163)TheKoebeDistortionTheoremandRelatedTopics
Chapter3.MiscellaneousProblems
1(164-174.2)VariousPropositions
2(175-179)AMethodofE.Landau
3(180-187)RectilinearApproachtoanEssentialSingularity
4(188-194)AsymptoticValuesofEntireFunctions
5(195-205)FurtherApplicationsofthePhragmen-LindelofMethod
6(206-212)SupplementaryProblems
PartFive.TheLocationofZeros
Chapter1.Rolle'sTheoremandDescartes'RuleofSigns
Problem
Numbers
1(1-21)ZerosofFunctions,ChangesofSignofSequences
2(22-27)ReversalsofSignofaFunction
3(28-41)FirstProofofDescartes'Rule.ofSigns
4(42-52)ApplicationsofDescartes'RuleofSigns
5(53-76)ApplicationsofRolle'sTheorem
6(77-86)Laguerre'sProofofDescartes'RuleofSigns
7(87-91)WhatistheBasisofDescartes'RuleofSigns?
8(92-100)GeneralizationsofRolie'sTheorem
Chapter2.TheGeometryoftheComplexPlaneandtheZerosofPolynomials
1(101-110)CenterofGravityofaSystemofPointswithrespecttoaPoint
2(111-127)CenterofGravityofaPolynomialwithrespecttoaPoint.ATheoremofLaguerre
3(128-156)DerivativeofaPolynomialwithrespecttoaPoint.
ATheoremofGrace
Chapter3.MiscellaneousProblems
1(157-182)ApproximationoftheZerosofTranscendentalFunctionsbytheZerosofRationalFunctions
2(183-189.3)PreciseDeterminationoftheNumberofZerosbyDescartes'RuleofSigns
3(190-196.1)AdditionalProblemsontheZerosofPolynomials
PartSix.PolynomialsandTrigonometricPolynomials
1(1-7)TchebychevPolynomials
2(8-15)GeneralProblemsonTrigonometricPolynomials
3(16-28)SomeSpecialTrigonometricPolynomials
4(29-38)SomeProblemsonFourierSeries
5(39-43)RealNon-negativeTrigonometricPolynomials
6(44-49)RealNon-negativePolynomials
7(50-61)Maximum-MinimumProblemsonTrigonometricPolynomials
8(62-66)Maximum-MinimumProblemsonPolynomials
9(67-76)TheLagrangeInterpolationFormula
10(77-83)TheTheoremsofS.BernsteinandA.Markov
11(84-102)LegendrePolynomialsandRelatedTopics
12(103-113)FurtherMaximum-MinimumProblemsonPolynomials
PartSeven.DeterminantsandQuadraticForms
Problem
Numbers
1(1-16)EvaluationofDeterminants.SolutionofLinearEquations
2(17-34)PowerSeriesExpansionofRationalFunctions
3(35-43.2)GenerationofPositiveQuadraticForms
4(44-54.4)MiscellaneousProblems
5(55-72)DeterminantsofSystemsofFunctionsPartEight.NumberTheory
Chapter1.ArithmeticalFunctions
1(1-11)ProblemsontheIntegralPartsofNumbers
2(12-20)CountingLatticePoints
3(21-27.2)ThePrincipleofInclusionandExclusion
4(28-37)PartsandDivisors
5(38-42)ArithmeticalFunctions,PowerSeries,DirichletSeries
6(43-64)MultiplicativeArithmeticalFunctions
7(65-78)LambertSeriesandRelatedTopics
8(79-83)FurtherProblemsonCountingLatticePoints
Chapter2.PolynomialswithIntegralCoefficientsandIntegral-ValuedFunctions
1(84-93)IntegralCoefficientsandIntegral-ValuedPolynomials
2(94-115)Integral-ValuedFunctionsandtheirPrimeDivisors
3(116-129)IrreducibilityofPolynomials
Chapter3.ArithmeticalAspectsofPowerSeries
1(130-137)PreparatoryProblemsonBinomialCoefficients
2(138-148)OnEisenstein'sTheorem
3(149-154)OntheProofofEisenstein'sTheorem
4(155-164)PowerSerieswithIntegralCoefficientsAssociatedwithRationalFunctions
5(165-173)Function-TheoreticAspectsofPowerSerieswithIntegralCoefficients
6(174-187)PowerSerieswithIntegralCoefficientsintheSenseofHurwitz
7(188-193)TheValuesattheIntegersofPowerSeriesthatConvergeaboutz=
Chapter4.SomeProblemsonAlgebraicIntegers
Problem
Numbers
1(194-203)AlgebraicIntegers.Fields
2(204-220)GreatestCommonDivisor
3(221-227.2)Congruences
4(228-237)ArithmeticalAspectsofPowerSeries
Chapter5.MiscellaneousProblems
1(237.1-244.4)LatticePointsinTwoandThreeDimensions
2(245-266)MiscellaneousProblems
PartNine.GeometricProblems
1(1-25)SomeGeometricProblems
Appendix
1AdditionalProblemstoPartOne
NewProblemsinEnglishEdition
AuthorIndex
SubjectIndex
Topics
Errata