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1、©StephenAbbottMathematicsDepartmentMiddleburyCollegeMiddlebury,VT05753USAabbott@middlebury.eduEditorialBoardS.AxlerF.W.GehringK.A.RibetMathematicsDepartmentMathematicsDepartmentMathematicsDepartmentSanFranciscoStateEastHallUniversityofCaliforniaUniversityUniversityofMichi
2、ganatBerkeleySanFrancisco,CA94132AnnArbor,MI48109Berkeley,CA94720-3840USAUSAUSAaxler@sfsu.edufgehring@math.lsa.ribet@math.berkeley.eduumich.eduMathematicsSubjectClassification(2000):2601LibraryofCongressCataloging-in-PublicationDataAbbott,Stephen,1964-Understandinganalysi
3、s/StephenAbbott.p.cm.—(Undergraduatetextsinmathematics)Includesbibliographicalreferencesandindex.1.Mathematicalanalysis.I.Title.II.Series.QA300.A182001515—dc2100-08308ISBN978-1-44I9-2866-5e-ISBN978-0-387-21506-8Printedonacid-freepaper.@2010SpringerScienceBusinessMedia,Inc
4、.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyfor
5、mofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasan
6、expressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.9876springeronline.comSpringerScience+BusinessPrefaceMyprimarygoalinwritingUnderstandingAnalysiswastocreateanelemen-taryone-semesterbookthatexposesstudentstotherichrewar
7、dsinherentintakingamathematicallyrigorousapproachtothestudyoffunctionsofarealvariable.Theaimofacourseinrealanalysisshouldbetochallengeandim-provemathematicalintuitionratherthantoverifyit.Thereisatendency,however,tocenteranintroductorycoursetoocloselyaroundthefamiliarthe-o
8、remsofthestandardcalculussequence.Producingarigorousargumentthatpolynomialsarecontinuousisgoodev
