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【全3册】分析123卷英文 阿莫恩 Analysis\/Herbert Amann 世界图书出版公司德国经典数学分析教材 分析基础教程 大学研究生数学教材
[德] 阿莫恩 (Amann H.) 著 / 世界图书出版公司 / 2012-09 / 平装
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分析(第1卷)
Thepresentbookstrivesforclarityandtransparency.Rightfromthebegin-ning,itrequiresfromthereaderawillingnesstodealwithabstractconcepts,aswellasaconsiderablemeasureofself-initiative.Forthesee&,rts,thereaderwillberichlyrewardedinhisorhermathematicalthinkingabilities,andwillpossessthefoundationneededforadeeperpenetrationintomathematicsanditsapplications.
Thisbookisthefirstvolumeofathreevolumeintroductiontoanalysis.Itde-velopedfrom.coursesthattheauthorshavetaughtoverthelasttwentysixyearsattheUniversitiesofBochum,Kiel,Zurich,BaselandKassel.Sincewehopethatthisbookwillbeusedalsoforself-studyandsupplementaryreading,wehaveincludedfarmorematerialthancanbecoveredinathreesemestersequence.Thisallowsustoprovideawideoverviewofthesubjectandtopresentthemanybeautifulandimportantapplicationsofthetheory.Wealsodemonstratethatmathematicspossesses,notonlyeleganceandinnerbeauty,butalsoprovidesefficientmethodsforthesolutionofconcreteproblems.
PrefaceChapterⅠFoundations1FundamentalsofLogic2SetsElementaryFactsThePowerSetComplement,IntersectionandUnionProductsFamiliesofSets3Functions,SimpleExamplesCompositionofFunctionsCommutativeDiagramsInjections,SurjectionsandBijectionsInverseFunctionsSetValuedFunctions4RelationsandOperationsEquivalenceRelationsOrderRelationsOperations5TheNaturalNumbersThePeanoAxiomsTheArithmeticofNaturalNumbersTheDivisionAlgorithmTheInductionPrincipleRecursiveDefinitions6CountabilityPermutationsEquinumerousSetsCountableSetsInfiniteProducts7GroupsandHomomorphismsGroupsSubgroupsCosetsHomomorphismsIsomorphisms8R.ings,FieldsandPolynomialsRingsTheBinomialTheoremTheMultinomialTheoremFieldsOrderedFieldsFormalPowerSeriesPolynomialsPolynomialFunctionsDivisionofPolynomiajsLinearFactorsPolynomialsinSeveralIndeterminates9TheRationalNumbersTheIntegersTheRationalNumbersRationalZerosofPolynomialsSquareRoots10TheRealNumbersOrderCompletenessDedekind'sConstructionoftheRealNumbersTheNaturalOrderonRTheExtendedNumberLineACharacterizationofSupremumandInfimumTheArchimedeanPropertyTheDensityoftheRationalNumbersinRnthRootsTheDensityoftheIrrationalNumbersinRIntervalsChapterⅡConvergenceChapterⅢContinuousFunctionsChapterⅣDifferentiationinOneVariableChapterⅤSequencesofFunctionsAppendixIntroductiontoMathematicalLogicBibliographyIndex
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