gtm012 advanced mathematical analysis

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1、GraduateTextsinMathematicsRichardBealsAdvancedMathematicalAnalysisSpringer-Verlag$7NewYorkHeidelbergBerlinGraduateTextsinMathematics12ManagingEditors:P.R.HalmosC.C.MooreRichardBealsAdvancedMathematicalAnalysisPeriodicFunctionsandDistributions,ComplexAnalysis,LaplaceTransformandApplicationsSpringer-

2、VerlagNewYorkHeidelbergBerlinRichardBealsProfessorofMathematicsUniversityofChicagoDepartmentofMathematics5734UniversityAvenueChicago,Illinois60637ManagingEditorsP.R.HalmosC.C.MooreIndianaUniversityUniversityofCaliforniaDepartmentofMathematicsatBerkeleySwainHallEastDepartmentofMathematicsBloomington

3、,Indiana47401Berkeley,California94720AMSSubjectClassification46-01,46S05,46C05,30-01,43-0134-01,3501LibraryofCongressCataloginginPublicationDataBeals,Richard,1938-Advancedmathematicalanalysis.(Graduatetextsinmathematics,v.12)1.Mathematicalanalysis.I.Title.II.Series.QA300.B451573-6884Allrightsreserv

4、ed.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.©1973bySpringer-VerlagNewYorkInc.PrintedintheUnitedStatesofAmerica.Second,correctedprinting.ISBN0-387-90066-7Springer-VerlagNewYorkHeidelbergBerlin(softcover)ISBN3-540-90066-7Springer-VerlagBerlinHeid

5、elbergNewYork(softcover)ISBN0-387-90065-9Springer-VerlagNewYorkHeidelbergBerlin(hardcover)ISBN3-540-90065-9Springer-VerlagBerlinHeidelbergNewYork(hardcover)toNancyPREFACEOnceuponatimestudentsofmathematicsandstudentsofscienceorengineeringtookthesamecoursesinmathematicalanalysisbeyondcalculus.Nowitis

6、commontoseparate"advancedmathematicsforscienceandengi-neering"fromwhatmightbecalled"advancedmathematicalanalysisformathematicians."Itseemstomebothusefulandtimelytoattemptareconciliation.Theseparationbetweenkindsofcourseshasunhealthyeffects.Mathe-maticsstudentsreversethehistoricaldevelopmentofanalys

7、is,learningtheunifyingabstractionsfirstandtheexampleslater(ifever).Sciencestudentslearntheexamplesastaughtgenerationsago,missingmoderninsights.AchoicebetweenencounteringFourierseriesasaminorinstanceoftherep