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1、GraduateTextsinMathematicsRichardBealsAdvancedMathematicalAnalysisSpringer-Verlag$7NewYorkHeidelbergBerlinGraduateTextsinMathematics12ManagingEditors:P.R.HalmosC.C.MooreRichardBealsAdvancedMathematicalAnalysisPeriodicFunctionsandDistributions,ComplexA
2、nalysis,LaplaceTransformandApplicationsSpringer-VerlagNewYorkHeidelbergBerlinRichardBealsProfessorofMathematicsUniversityofChicagoDepartmentofMathematics5734UniversityAvenueChicago,Illinois60637ManagingEditorsP.R.HalmosC.C.MooreIndianaUniversityUniver
3、sityofCaliforniaDepartmentofMathematicsatBerkeleySwainHallEastDepartmentofMathematicsBloomington,Indiana47401Berkeley,California94720AMSSubjectClassification46-01,46S05,46C05,30-01,43-0134-01,3501LibraryofCongressCataloginginPublicationDataBeals,Richa
4、rd,1938-Advancedmathematicalanalysis.(Graduatetextsinmathematics,v.12)1.Mathematicalanalysis.I.Title.II.Series.QA300.B451573-6884Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.©1973byS
5、pringer-VerlagNewYorkInc.PrintedintheUnitedStatesofAmerica.Second,correctedprinting.ISBN0-387-90066-7Springer-VerlagNewYorkHeidelbergBerlin(softcover)ISBN3-540-90066-7Springer-VerlagBerlinHeidelbergNewYork(softcover)ISBN0-387-90065-9Springer-VerlagNew
6、YorkHeidelbergBerlin(hardcover)ISBN3-540-90065-9Springer-VerlagBerlinHeidelbergNewYork(hardcover)toNancyPREFACEOnceuponatimestudentsofmathematicsandstudentsofscienceorengineeringtookthesamecoursesinmathematicalanalysisbeyondcalculus.Nowitiscommontosep
7、arate"advancedmathematicsforscienceandengi-neering"fromwhatmightbecalled"advancedmathematicalanalysisformathematicians."Itseemstomebothusefulandtimelytoattemptareconciliation.Theseparationbetweenkindsofcourseshasunhealthyeffects.Mathe-maticsstudentsre
8、versethehistoricaldevelopmentofanalysis,learningtheunifyingabstractionsfirstandtheexampleslater(ifever).Sciencestudentslearntheexamplesastaughtgenerationsago,missingmoderninsights.AchoicebetweenencounteringFourierseriesasaminorinstanceoftherep
