elementary real analysis (dripped) thompson bruckner外语英文电子书

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1、ELEMENTARYREALANALYSIS:DRIPPEDVERSION—————————————thomson·bruckner2—————————————BrianS.ThomsonJudithB.BrucknerAndrewM.Brucknerwww.classicalrealanalysis.com(2008)D.R.I.P.=DumptheRiemannIntegralProject.Thisversionofthetextincludesanaccountofthenaturalintegralonthereal

2、lineandremovesthedevelopmentoftheRiemannintegralandtheimproperRiemannintegral.Itshouldbeconsideredexperimental.cThisPDFfileincludesmaterialfromthetextElementaryRealAnalysisoriginallypublishedbyPrenticeHall(Pearson)in2001.Theauthorsretainthecopyrightandallcommercialu

3、ses.[2008]DatePDFfilecompiled:December25,2007CONTENTSPREFACExvi1PROPERTIESOFTHEREALNUMBERS11.1Introduction11.2TheRealNumberSystem21.3AlgebraicStructure51.4OrderStructure81.5Bounds91.6SupsandInfs111.7TheArchimedeanProperty141.8InductivePropertyofIN161.9TheRationalNumb

4、ersAreDense171.10TheMetricStructureofR191.11ChallengingProblemsforChapter1212SEQUENCES242.1Introduction242.2Sequences262.2.1SequenceExamples272.3CountableSets312.4Convergence342.5Divergence392.6BoundednessPropertiesofLimits412.7AlgebraofLimits432.8OrderPropertiesofL

5、imits492.9MonotoneConvergenceCriterion542.10ExamplesofLimits58iiiiv2.11Subsequences632.12CauchyConvergenceCriterion682.13UpperandLowerLimits712.14ChallengingProblemsforChapter2773INFINITESUMS803.1Introduction803.2FiniteSums813.3InfiniteUnorderedsums873.3.1CauchyCrite

6、rion893.4OrderedSums:Series933.4.1Properties943.4.2SpecialSeries953.5CriteriaforConvergence1023.5.1BoundednessCriterion1023.5.2CauchyCriterion1033.5.3AbsoluteConvergence1043.6TestsforConvergence1083.6.1TrivialTest1083.6.2DirectComparisonTests1093.6.3LimitComparisonT

7、ests1113.6.4RatioComparisonTest1123.6.5d’Alembert’sRatioTest1133.6.6Cauchy’sRootTest1153.6.7Cauchy’sCondensationTest1173.6.8IntegralTest1183.6.9Kummer’sTests1203.6.10Raabe’sRatioTest1223.6.11Gauss’sRatioTest1233.6.12AlternatingSeriesTest1253.6.13Dirichlet’sTest1273.

8、6.14Abel’sTest1283.7Rearrangements1343.7.1UnconditionalConvergence1353.7.2ConditionalConvergence136

∞3.7.3Comparisonofi=1aiandi∈INai1373.