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1、PrinciplesofMathematicalAnalysis(数学分析原理）,THIRDEDITION,WALTERRUDIN著 这是一部现代数学名著，一直受到数学界的推崇。作为Rudin的分析学经典著作之一，本书在西方各国乃至我国均有着广泛而深远的影响，被许多高校用做数学分析课的必选教材。本书涵盖了高等微积分学的丰富内容，最精彩的部分集中在基础拓扑结构、函数项序列与级数、多变量函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯与思考方式。 本书内容相当精练，结构简单明了，这也是Rudin著作
2、的一大特色。与其说这是一部教科书，不如说这是一部字典。英文版的PREFACEThisbookisintendedtoserveasatextforthecourseinanalysisthatisusuallytakenbyadvancedundergraduatesorbyfirst-yearstudentswhostudymathe-matics.Thepresenteditioncoversessentiallythesametopicsasthesecondone,withsomeadditions,afewminoromi
3、ssions,andconsiderablerearrangement.Ihopethatthesechangeswillmakethematerialmoreaccessibleamdmoreattractivetothestudentswhotakesuchacourse.Experiencehasconvincedmethatitispedagogicallyunsound(thoughlogicallycorrect)tostartoffwiththeconstructionoftherealnumbersfromthera
4、tionalones.Atthebeginning,moststudentssimplyfailtoappreciatetheneedfordoingthis.Accordingly,therealnumbersystemisintroducedasanorderedfieldwiththeleast-upper-boundproperty,andafewinterestingapplicationsof thispropertyarequicklymade.However,Dedekind'sconstructionisnotom
5、itted.ItisnowinanAppendixtoChapter1,whereitmaybestudiedandenjoyedwheneverthetimeseemsripe.Thematerialonfunctionsofseveralvariablesisalmostcompletelyrewritten,withmanydetailsfilledin,andwithmoreexamplesandmoremotivation.Theproofoftheinversefunctiontheorem--thekeyiteminC
6、hapter9--isXPREFACEsimplifiedbymeansofthefixedpointtheoremaboutcontractionmappings.Differentialformsarediscussedinmuchgreaterdetail.SeveralapplicationsofStokes'theoremareincluded.Asregardsotherchanges,thechapterontheRiemann-Stieltjesintegralhasbeentrimmedabit,ashortdo-
7、it-yourselfsectiononthegammafunctionhasbeenaddedtoChapter8,andthereisalargenumberofnewexercises,most ofthemwithfairlydetailedhints.IhavealsoincludedseveralreferencestoarticlesappearingintheAmericanMathematicalMonthlyandinMathematicsMagazine,inthehopethatstudentswilldev
8、elopthehabitoflookingintothejournalliterature.MostofthesereferenceswerekindlysuppliedbyR.B.Burckel.Overtheyears,manyp
