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首页 [国外英语本科数学教材.微积分.斯图尔特.第六版].Calculus.Stewart.Trans…

[国外英语本科数学教材.微积分.斯图尔特.第六版].Calculus.Stewart.Transcend.pdf

[国外英语本科数学教材.微积分.斯图尔特.第六版].Calcu…

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2012-01-06 0人阅读 举报 0 0 暂无简介

简介:本文档为《[国外英语本科数学教材.微积分.斯图尔特.第六版].Calculus.Stewart.Transcendpdf》,可适用于高等教育领域

AUSTRALIANBRAZILNCANADANMEXICONSINGAPORENSPAINNUNITEDKINGDOMNUNITEDSTATESCALCULUSEARLYTRANSCENDENTALSSIXTHEDITIONJAMESSTEWARTMcMASTERUNIVERSITYPublisherNBobPirtleAssistantEditorNStacyGreenEditorialAssistantNElizabethRodioTechnologyProjectManagerNSamSubityMarketingManagerNMarkSanteeMarketingAssistantNMelissaWongMarketingCommunicationsManagerNBryanVannProjectManager,EditorialProductionNCheryllLinthicumCreativeDirectorNRobHugelArtDirectorNVernonTBoesPrintBuyerNBeckyCrossPermissionsEditorNBobKauserProductionServiceNTECH·artsTextDesignerNKathiTownesPhotoResearcherNStephanieKuhnsCopyEditorNKathiTownesIllustratorNBrianBetsillCoverDesignerNIreneMorrisCoverImageNAmelieFear,FolkmusiciancomCoverPrinterNRRDonnelleyWillardCompositorNStephanieKuhns,TECH·artsPrinterNRRDonnelleyWillardTrademarksExamView®andExamViewPro®areregisteredtrademarksofFSCreations,IncWindowsisaregisteredtrademarkoftheMicrosoftCorporationandusedhereinunderlicenseMacintoshandPowerMacintoshareregisteredtrademarksofAppleComputer,IncUsedhereinunderlicenseDeriveisaregisteredtrademarkofSoftWarehouse,IncMapleisaregisteredtrademarkofWaterlooMaple,IncMathematicaisaregisteredtrademarkofWolframResearch,IncToolsforEnrichingisatrademarkusedhereinunderlicenseThomsonHigherEducationDavisDriveBelmont,CAUSACOPYRIGHT©,ThomsonBrooksCole,apartofTheThomsonCorporationThomson,theStarlogo,andBrooksColearetrademarksusedhereinunderlicenseALLRIGHTSRESERVEDNopartofthisworkcoveredbythecopyrighthereonmaybereproducedorusedinanyformorbyanymeansgraphic,electronic,ormechanical,includingphotocopying,recording,taping,webdistribution,informationstorageandretrievalsystems,orinanyothermannerwithoutthewrittenpermissionofthepublisherPrintedintheUnitedStatesofAmerica©ThomsonLearning,IncAllRightsReservedThomsonLearningWebTutor™isatrademarkofThomsonLearning,IncLibraryofCongressControlNumber:ISBN:ISBN:Formoreinformationaboutourproducts,contactusat:ThomsonLearningAcademicResourceCenterForpermissiontousematerialfromthistextorproduct,submitarequestonlineathttp:wwwthomsonrightscomAnyadditionalquestionsaboutpermissionscanbesubmittedbyemailtothomsonrightsthomsoncomKTCalculusEarlyTranscendentals,eJamesStewartiiiPrefacexiTotheStudentxxiiiDiagnosticTestsxxivAPREVIEWOFCALCULUSFUNCTIONSANDMODELSFourWaystoRepresentaFunctionMathematicalModels:ACatalogofEssentialFunctionsNewFunctionsfromOldFunctionsGraphingCalculatorsandComputersExponentialFunctionsInverseFunctionsandLogarithmsReviewPrinciplesofProblemSolvingLIMITSANDDERIVATIVESTheTangentandVelocityProblemsTheLimitofaFunctionCalculatingLimitsUsingtheLimitLawsThePreciseDefinitionofaLimitContinuityLimitsatInfinityHorizontalAsymptotesDerivativesandRatesofChangeWritingProjectNEarlyMethodsforFindingTangentsTheDerivativeasaFunctionReviewProblemsPlusCONTENTSDIFFERENTIATIONRULESDerivativesofPolynomialsandExponentialFunctionsAppliedProjectNBuildingaBetterRollerCoasterTheProductandQuotientRulesDerivativesofTrigonometricFunctionsTheChainRuleAppliedProjectNWhereShouldaPilotStartDescentImplicitDifferentiationDerivativesofLogarithmicFunctionsRatesofChangeintheNaturalandSocialSciencesExponentialGrowthandDecayRelatedRatesLinearApproximationsandDifferentialsLaboratoryProjectNTaylorPolynomialsHyperbolicFunctionsReviewProblemsPlusAPPLICATIONSOFDIFFERENTIATIONMaximumandMinimumValuesAppliedProjectNTheCalculusofRainbowsTheMeanValueTheoremHowDerivativesAffecttheShapeofaGraphIndeterminateFormsandL’Hospital’sRuleWritingProjectNTheOriginsofL’Hospital’sRuleSummaryofCurveSketchingGraphingwithCalculusandCalculatorsOptimizationProblemsAppliedProjectNTheShapeofaCanNewton’sMethodAntiderivativesReviewProblemsPlusyπm=m=m=πππiv||||CONTENTSCONTENTS||||vINTEGRALSAreasandDistancesTheDefiniteIntegralDiscoveryProjectNAreaFunctionsTheFundamentalTheoremofCalculusIndefiniteIntegralsandtheNetChangeTheoremWritingProjectNNewton,Leibniz,andtheInventionofCalculusTheSubstitutionRuleReviewProblemsPlusINTEGRALSAreasbetweenCurvesVolumesVolumesbyCylindricalShellsWorkAverageValueofaFunctionAppliedProjectNWheretoSitattheMoviesReviewProblemsPlusTECHNIQUESOFINTEGRATIONIntegrationbyPartsTrigonometricIntegralsTrigonometricSubstitutionIntegrationofRationalFunctionsbyPartialFractionsStrategyforIntegrationIntegrationUsingTablesandComputerAlgebraSystemsDiscoveryProjectNPatternsinIntegralsvi||||CONTENTSApproximateIntegrationImproperIntegralsReviewProblemsPlusFURTHERAPPLICATIONSOFINTEGRATIONArcLengthDiscoveryProjectNArcLengthContestAreaofaSurfaceofRevolutionDiscoveryProjectNRotatingonaSlantApplicationstoPhysicsandEngineeringDiscoveryProjectNComplementaryCoffeeCupsApplicationstoEconomicsandBiologyProbabilityReviewProblemsPlusDIFFERENTIALEQUATIONSModelingwithDifferentialEquationsDirectionFieldsandEuler’sMethodSeparableEquationsAppliedProjectNHowFastDoesaTankDrainAppliedProjectNWhichIsFaster,GoingUporComingDownModelsforPopulationGrowthAppliedProjectNCalculusandBaseballLinearEquationsPredatorPreySystemsReviewProblemsPlusPARAMETRICEQUATIONSANDPOLARCOORDINATESCurvesDefinedbyParametricEquationsLaboratoryProjectNRunningCirclesaroundCirclesCalculuswithParametricCurvesLaboratoryProjectNBézierCurvesPolarCoordinatesAreasandLengthsinPolarCoordinatesConicSectionsConicSectionsinPolarCoordinatesReviewProblemsPlusINFINITESEQUENCESANDSERIESSequencesLaboratoryProjectNLogisticSequencesSeriesTheIntegralTestandEstimatesofSumsTheComparisonTestsAlternatingSeriesAbsoluteConvergenceandtheRatioandRootTestsStrategyforTestingSeriesPowerSeriesRepresentationsofFunctionsasPowerSeriesTaylorandMaclaurinSeriesLaboratoryProjectNAnElusiveLimitWritingProjectNHowNewtonDiscoveredtheBinomialSeriesApplicationsofTaylorPolynomialsAppliedProjectNRadiationfromtheStarsReviewProblemsPlusCONTENTS||||viiviii||||CONTENTSVECTORSANDTHEGEOMETRYOFSPACEThreeDimensionalCoordinateSystemsVectorsTheDotProductTheCrossProductDiscoveryProjectNTheGeometryofaTetrahedronEquationsofLinesandPlanesLaboratoryProjectNPuttingDinPerspectiveCylindersandQuadricSurfacesReviewProblemsPlusVECTORFUNCTIONSVectorFunctionsandSpaceCurvesDerivativesandIntegralsofVectorFunctionsArcLengthandCurvatureMotioninSpace:VelocityandAccelerationAppliedProjectNKepler’sLawsReviewProblemsPlusPARTIALDERIVATIVESFunctionsofSeveralVariablesLimitsandContinuityPartialDerivativesTangentPlanesandLinearApproximationsTheChainRuleDirectionalDerivativesandtheGradientVectorMaximumandMinimumValuesAppliedProjectNDesigningaDumpsterDiscoveryProjectNQuadraticApproximationsandCriticalPointsLONDONOPARISCONTENTS||||ixLagrangeMultipliersAppliedProjectNRocketScienceAppliedProjectNHydroTurbineOptimizationReviewProblemsPlusMULTIPLEINTEGRALSDoubleIntegralsoverRectanglesIteratedIntegralsDoubleIntegralsoverGeneralRegionsDoubleIntegralsinPolarCoordinatesApplicationsofDoubleIntegralsTripleIntegralsDiscoveryProjectNVolumesofHyperspheresTripleIntegralsinCylindricalCoordinatesDiscoveryProjectNTheIntersectionofThreeCylindersTripleIntegralsinSphericalCoordinatesAppliedProjectNRollerDerbyChangeofVariablesinMultipleIntegralsReviewProblemsPlusVECTORCALCULUSVectorFieldsLineIntegralsTheFundamentalTheoremforLineIntegralsGreen’sTheoremCurlandDivergenceParametricSurfacesandTheirAreasSurfaceIntegralsStokes’TheoremWritingProjectNThreeMenandTwoTheoremsx||||CONTENTSTheDivergenceTheoremSummaryReviewProblemsPlusSECONDORDERDIFFERENTIALEQUATIONSSecondOrderLinearEquationsNonhomogeneousLinearEquationsApplicationsofSecondOrderDifferentialEquationsSeriesSolutionsReviewAPPENDIXESAANumbers,Inequalities,andAbsoluteValuesABCoordinateGeometryandLinesACGraphsofSecondDegreeEquationsADTrigonometryAESigmaNotationAFProofsofTheoremsAGTheLogarithmDefinedasanIntegralAHComplexNumbersAIAnswerstoOddNumberedExercisesAINDEXAxiAgreatdiscoverysolvesagreatproblembutthereisagrainofdiscoveryinthesolutionofanyproblemYourproblemmaybemodestbutifitchallengesyourcuriosityandbringsintoplayyourinventivefaculties,andifyousolveitbyyourownmeans,youmayexperiencethetensionandenjoythetriumphofdiscoveryGEORGEPOLYAPREFACETheartofteaching,MarkVanDorensaid,istheartofassistingdiscoveryIhavetriedtowriteabookthatassistsstudentsindiscoveringcalculusbothforitspracticalpoweranditssurprisingbeautyInthisedition,asinthefirstfiveeditions,Iaimtoconveytothestudentasenseoftheutilityofcalculusanddeveloptechnicalcompetence,butIalsostrivetogivesomeappreciationfortheintrinsicbeautyofthesubjectNewtonundoubtedlyexperiencedasenseoftriumphwhenhemadehisgreatdiscoveriesIwantstudentstosharesomeofthatexcitementTheemphasisisonunderstandingconceptsIthinkthatnearlyeverybodyagreesthatthisshouldbetheprimarygoalofcalculusinstructionInfact,theimpetusforthecurrentcalculusreformmovementcamefromtheTulaneConferencein,whichformulatedastheirfirstrecommendation:FocusonconceptualunderstandingIhavetriedtoimplementthisgoalthroughtheRuleofThree:“Topicsshouldbepresentedgeometrically,numerically,andalgebraically”Visualization,numericalandgraphicalexperimentation,andotherapproacheshavechangedhowweteachconceptualreasoninginfundamentalwaysMorerecently,theRuleofThreehasbeenexpandedtobecometheRuleofFourbyemphasizingtheverbal,ordescriptive,pointofviewaswellInwritingthesixtheditionmypremisehasbeenthatitispossibletoachieveconceptualunderstandingandstillretainthebesttraditionsoftraditionalcalculusThebookcontainselementsofreform,butwithinthecontextofatraditionalcurriculumALTERNATIVEVERSIONSIhavewrittenseveralothercalculustextbooksthatmightbepreferableforsomeinstructorsMostofthemalsocomeinsinglevariableandmultivariableversionsNCalculus,SixthEdition,issimilartothepresenttextbookexceptthattheexponential,logarithmic,andinversetrigonometricfunctionsarecoveredinthesecondsemesterNEssentialCalculusisamuchbrieferbook(pages),thoughitcontainsalmostallofthetopicsinCalculus,SixthEditionTherelativebrevityisachievedthroughbrieferexpositionofsometopicsandputtingsomefeaturesonthewebsiteNEssentialCalculus:EarlyTranscendentalsresemblesEssentialCalculus,buttheexponential,logarithmic,andinversetrigonometricfunctionsarecoveredinChapterxii||||PREFACENCalculus:ConceptsandContexts,ThirdEdition,emphasizesconceptualunderstandingevenmorestronglythanthisbookThecoverageoftopicsisnotencyclopedicandthematerialontranscendentalfunctionsandonparametricequationsiswoventhroughoutthebookinsteadofbeingtreatedinseparatechaptersNCalculus:EarlyVectorsintroducesvectorsandvectorfunctionsinthefirstsemesterandintegratesthemthroughoutthebookItissuitableforstudentstakingEngineeringandPhysicscoursesconcurrentlywithcalculusWHAT’SNEWINTHESIXTHEDITIONHerearesomeofthechangesforthesixtheditionofCalculus:EarlyTranscendentalsNAtthebeginningofthebooktherearefourdiagnostictests,inBasicAlgebra,AnalyticGeometry,Functions,andTrigonometryAnswersaregivenandstudentswhodon’tdowellarereferredtowheretheyshouldseekhelp(Appendixes,reviewsectionsofChapter,andthewebsite)NInresponsetorequestsofseveralusers,thematerialmotivatingthederivativeisbriefer:SectionsandarecombinedintoasinglesectioncalledDerivativesandRatesofChangeNThesectiononHigherDerivativesinChapterhasdisappearedandthatmaterialisintegratedintovarioussectionsinChaptersandNInstructorswhodonotcoverthechapterondifferentialequationshavecommentedthatthesectiononExponentialGrowthandDecaywasinconvenientlylocatedthereAccordingly,itismovedearlierinthebook,toChapterThismoveprecipitatesareorganizationofChaptersandNSectionsandaremergedintoasinglesection,withabriefertreatmentofoptimizationproblemsinbusinessandeconomicsNSectionsandaremergedintoasinglesectionIhadpreviouslyfeaturedthebinomialseriesinitsownsectiontoemphasizeitsimportanceButIlearnedthatsomeinstructorswereomittingthatsection,soIhavedecidedtoincorporatebinomialseriesintoNThematerialoncylindricalandsphericalcoordinates(formerlySection)ismovedtoChapter,whereitisintroducedinthecontextofevaluatingtripleintegralsNNewphrasesandmarginnoteshavebeenaddedtoclarifytheexpositionNAnumberofpiecesofarthavebeenredrawnNThedatainexamplesandexerciseshavebeenupdatedtobemoretimelyNManyexampleshavebeenaddedorchangedForinstance,ExampleonpagewaschangedbecausestudentsareoftenbaffledwhentheyseearbitraryconstantsinaproblemandIwantedtogiveanexampleinwhichtheyoccurNExtrastepshavebeenprovidedinsomeoftheexistingexamplesNMorethanoftheexercisesineachchapterarenewHereareafewofmyfavorites:,,,,,,,and–NTherearealsosomegoodnewproblemsintheProblemsPlussectionsSee,forinstance,Problemsandonpage,Problemonpage,andProblemonpageNThenewprojectonpage,ComplementaryCoffeeCups,comesfromanarticlebyThomasBanchoffinwhichhewonderedwhichoftwocoffeecups,whoseconvexandconcaveprofilesfittogethersnugly,wouldholdmorecoffeePREFACE||||xiiiNToolsforEnrichingCalculus(TEC)hasbeencompletelyredesignedandisaccessibleontheInternetatwwwstewartcalculuscomItnowincludeswhatwecallVisuals,briefanimationsofvariousfiguresinthetextInaddition,therearenowVisual,Modules,andHomeworkHintsforthemultivariablechaptersSeethedescriptiononpagexivNThesymbolhasbeenplacedbesideexamples(anaverageofthreepersection)forwhichtherearevideosofinstructorsexplainingtheexampleinmoredetailThismaterialisalsoavailableonDVDSeethedescriptiononpagexxiFEATURESCONCEPTUALEXERCISESThemostimportantwaytofosterconceptualunderstandingisthroughtheproblemsthatweassignTothatendIhavedevisedvarioustypesofproblemsSomeexercisesetsbeginwithrequeststoexplainthemeaningsofthebasicconceptsofthesection(See,forinstance,thefirstfewexercisesinSections,,,,and)Similarly,allthereviewsectionsbeginwithaConceptCheckandaTrueFalseQuizOtherexercisestestconceptualunderstandingthroughgraphsortables(seeExercises,–,–,–,–,,–,–,–,–,–,–,–,–,–,–,and–)Anothertypeofexerciseusesverbaldescriptiontotestconceptualunderstanding(seeExercises,,–,and)Iparticularlyvalueproblemsthatcombineandcomparegraphical,numerical,andalgebraicapproaches(seeExercises–,,and)GRADEDEXERCISESETSEachexercisesetiscarefullygraded,progressingfrombasicconceptualexercisesandskilldevelopmentproblemstomorechallengingproblemsinvolvingapplicationsandproofsREALWORLDDATAMyassistantsandIspentagreatdealoftimelookinginlibraries,contactingcompaniesandgovernmentagencies,andsearchingtheInternetforinterestingrealworlddatatointroduce,motivate,andillustratetheconceptsofcalculusAsaresult,manyoftheexamplesandexercisesdealwithfunctionsdefinedbysuchnumericaldataorgraphsSee,forinstance,FigureinSection(seismogramsfromtheNorthridgeearthquake),Exercise(percentageofthepopulationunderage),Exercise(velocityofthespaceshuttleEndeavour),andFigureinSection(SanFranciscopowerconsumption)Functionsoftwovariablesareillustratedbyatableofvaluesofthewindchillindexasafunctionofairtemperatureandwindspeed(ExampleinSection)PartialderivativesareintroducedinSectionbyexaminingacolumninatableofvaluesoftheheatindex(perceivedairtemperature)asafunctionoftheactualtemperatureandtherelativehumidityThisexampleispursuedfurtherinconnectionwithlinearapproximations(ExampleinSection)DirectionalderivativesareintroducedinSectionbyusingatemperaturecontourmaptoestimatetherateofchangeoftemperatureatRenointhedirectionofLasVegasDoubleintegralsareusedtoestimatetheaveragesnowfall

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[国外英语本科数学教材.微积分.斯图尔特.第六版].Calculus.Stewart.Transcend

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