gtm012.beals.r..advanced.mathematical.analysis.(springer.1973)(isbn.0387900659)(t)(243s)

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

2、sSpringer-VerlagNewYorkHeidelbergBerlinRichardBealsProfessorofMathematicsUniversityofChicagoDepartmentofMathematics5734UniversityAvenueChicago,Illinois60637ManagingEditorsP.R.HalmosC.C.MooreIndianaUniversityUniversityofCaliforniaDepartmentofMathematicsatBerkeleySwainHallEastDepartmentofMa

3、thematicsBloomington,Indiana47401Berkeley,California94720AMSSubjectClassification46-01,46S05,46C05,30-01,43-0134-01,3501LibraryofCongressCataloginginPublicationDataBeals,Richard,1938-Advancedmathematicalanalysis.(Graduatetextsinmathematics,v.12)1.Mathematicalanalysis.I.Title.II.Series.QA3

4、00.B451573-6884Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.©1973bySpringer-VerlagNewYorkInc.PrintedintheUnitedStatesofAmerica.Second,correctedprinting.ISBN0-387-90066-7Springer-VerlagNewYorkHeidelbergBerlin(softcover)IS

5、BN3-540-90066-7Springer-VerlagBerlinHeidelbergNewYork(softcover)ISBN0-387-90065-9Springer-VerlagNewYorkHeidelbergBerlin(hardcover)ISBN3-540-90065-9Springer-VerlagBerlinHeidelbergNewYork(hardcover)toNancyPREFACEOnceuponatimestudentsofmathematicsandstudentsofscienceorengineeringtookthesamec

6、oursesinmathematicalanalysisbeyondcalculus.Nowitiscommontoseparate"advancedmathematicsforscienceandengi-neering"fromwhatmightbecalled"advancedmathematicalanalysisformathematicians."Itseemstomebothusefulandtimelytoattemptareconciliation.Theseparationbetweenkindsofcourseshasunhealthyeffects

7、.Mathe-maticsstudentsreversethehistoricaldevelopmentofanalysis,learningtheunifyingabstractionsfirstandtheexampleslater(ifever).Sciencestudentslearntheexamplesastaughtgenerationsago,missingmoderninsights.AchoicebetweenencounteringFourierseriesasaminorinstanceoftherep