introduction to real analysis(william)

《introduction to real analysis(william)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、INTRODUCTIONTOREALANALYSISWilliamF.TrenchProfessorEmeritusTrinityUniversitySanAntonio,TX,USA©2003WilliamF.Trench,allrightsreservedLibraryofCongressCataloging-in-PublicationDataTrench,WilliamF.Introductiontorealanalysis/WilliamF.Trenchp.cm.ISBN0-13-045786-81.MathematicalAnalysis.I.Title

2、.QA300.T6672003515-dc212002032369FreeEdition1,March2009ThisbookwaspublishedpreviouslybyPearsonEducation.Thisfreeeditionismadeavailableinthehopethatitwillbeusefulasatextbookorrefer-ence.Reproductionispermittedforanyvalidnoncommercialeducational,mathematical,orscientificpurpose.Itmaybepos

3、tedonfacultywebpagesforconvenienceofstudentdownloads.However,saleorchargesforprofitbeyondreasonableprintingcostsarepro-hibited.Acompleteinstructor’ssolutionmanualisavailablebyemailtowtrench@trinity.edu,sub-jecttoverificationoftherequestor’sfacultystatus.TOBEVERLYContentsPrefaceviChapter1

4、TheRealNumbers11.1TheRealNumberSystem11.2MathematicalInduction101.3TheRealLine19Chapter2DifferentialCalculusofFunctionsofOneVariable302.1FunctionsandLimits302.2Continuity532.3DifferentiableFunctionsofOneVariable732.4L’Hospital’sRule882.5Taylor’sTheorem98Chapter3IntegralCalculusofFunction

5、sofOneVariable1133.1DefinitionoftheIntegral1133.2ExistenceoftheIntegral1283.3PropertiesoftheIntegral1353.4ImproperIntegrals1513.5AMoreAdvancedLookattheExistenceoftheProperRiemannIntegral171Chapter4InfiniteSequencesandSeries1784.1SequencesofRealNumbers1794.2EarlierTopicsRevisitedWithSeque

6、nces195ivContentsv4.3InfiniteSeriesofConstants2004.4SequencesandSeriesofFunctions2344.5PowerSeries257Chapter5Real-ValuedFunctionsofSeveralVariables2815.1StructureofRn2815.2ContinuousReal-ValuedFunctionofnVariables3025.3PartialDerivativesandtheDifferential3165.4TheChainRuleandTaylor’sTheo

7、rem339Chapter6Vector-ValuedFunctionsofSeveralVariables3616.1LinearTransformationsandMatrices3616.2ContinuityandDifferentiabilityofTransformations3786.3TheInverseFunctionTheorem3946.4TheImplicitFunctionTheorem417Chapter7IntegralsofFunctionsofSeveralVariables4357.1DefinitionandExistenceo