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1、RogerGodementAnalysisIIDifferentialandIntegralCalculus,FourierSeries,HolomorphicFunctionsABCRogerGodementDépartementdeMathématiquesUniversitéParisVII2,placeJussieu75251ParisCedex05FranceE-mail:rgodement@aol.comTranslatorPhilipSpainMathematicsDepartmentUniversityofGlasgowGlasgowG128QWScotlandE-mail:p
2、gs@maths.gla.ac.ukMathematicsSubjectClassification2000:26-01,26A03,26A05,26A09,26A12,26A15,26A24,26A42,26B05,28-XX,30-XX,30-01,31-XX,32-XX,41-XX,42-XX,41-01,43-XX,44-XX,54-XXLibraryofCongressControlNumber:2003066673ISBN-103-540-20921-2SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-20921-8SpringerBer
3、linHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpart
4、sthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringeronline.comcSpringer-VerlagBerli
5、nHeidelberg2005PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandTechBooksus
6、ingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1086673341/TechBooks543210ContentsV–DifferentialandIntegralCalculus........................1§1.TheRiemannIntegral...................................11–Upperandlowerintegralsofaboundedfunction........1
7、2–Elementarypropertiesofintegrals.....................53–Riemannsums.Theintegralnotation..................144–Uniformlimitsofintegrablefunctions..................165–ApplicationtoFourierseriesandtopow
