calculusearlytranscendentalsbyjamesstewart部分1Word文档格式.docx
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calculusearlytranscendentalsbyjamesstewart部分1Word文档格式.docx
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ThomsonLearningAcademicResourceCenter1-800-423-0563Forpermissiontousematerialfromthistextorproduct,submitarequestonlineatadditionalquestionsaboutpermissionscanbesubmittedbyemailtothomsonrights@.K05T07CalculusEarlyTranscendentals,6eJamesStewart
iiiPrefacexiTotheStudentxxiiiDiagnosticTestsxxivAPREVIEWOFCALCULUS2FUNCTIONSANDMODELS101.1FourWaystoRepresentaFunctionMathematicalModels:
ACatalogofEssentialFunctionsNewFunctionsfromOldFunctionsGraphingCalculatorsandComputersExponentialFunctions52InverseFunctionsandLogarithmsReview73111.2241.3371.4461.51.659PrinciplesofProblemSolving76LIMITSANDDERIVATIVES822.1TheTangentandVelocityProblemsTheLimitofaFunctionCalculatingLimitsUsingtheLimitLawsThePreciseDefinitionofaLimitContinuity119LimitsatInfinity;
HorizontalAsymptotesDerivativesandRatesofChangeWritingProject832.2882.3992.41092.52.61302.7143NEarlyMethodsforFindingTangents1532.8TheDerivativeasaFunction154Review165ProblemsPlus17021CONTENTS文库
DIFFERENTIATIONRULES1723.1DerivativesofPolynomialsandExponentialFunctions173AppliedProjectNBuildingaBetterRollerCoaster1823.2TheProductandQuotient
Rules1833.3DerivativesofTrigonometricFunctions1893.4TheChainRule197AppliedProjectNWhereShouldaPilotStartDescent?
2063.5ImplicitDifferentiation2073.6DerivativesofLogarithmicFunctions2153.7RatesofChangeintheNaturalandSocialSciences2213.8ExponentialGrowthandDecay2333.9RelatedRates2413.10LinearApproximationsandDifferentials247LaboratoryProjectNTaylorPolynomials2533.11HyperbolicFunctions254Review261ProblemsPlus265APPLICATIONSOFDIFFERENTIATION2704.1MaximumandMinimumValues271AppliedProjectNTheCalculusofRainbows2794.2TheMeanValueTheorem2804.3HowDerivativesAffecttheShapeofaGraph2874.4IndeterminateFormsandL’
Hospital’sRule298WritingProjectNTheOriginsofL’Hospital’sRule3074.5SummaryofCurve
Sketching3074.6GraphingwithCalculusandCalculatorsOptimization
Problems3154.7322AppliedProjectNTheShapeofaCan3334.8Newton’s
Method3344.9Antiderivatives340Review347Problems
Plus351430y0π2m=1m=_1πm=0π2πiv||||CONTENTS
CONTENTS||||vINTEGRALS3545.1AreasandDistances3555.2TheDefiniteIntegral366DiscoveryProjectNAreaFunctions3795.3TheFundamentalTheoremofCalculus3795.4IndefiniteIntegralsandtheNetChangeTheorem391WritingProjectNNewton,Leibniz,andtheInventionofCalculus3995.5TheSubstitutionRule400Review408ProblemsPlus412INTEGRALS4146.1AreasbetweenCurves4156.2Volumes4226.3VolumesbyCylindricalShells4336.4Work4386.5AverageValueofaFunction442AppliedProjectNWheretoSitattheMovies446Review446ProblemsPlus448.TECHNIQUESOFINTEGRATION4527.1IntegrationbyParts4537.2TrigonometricIntegrals4607.3TrigonometricSubstitution4677.4IntegrationofRationalFunctionsbyPartialFractions4737.5StrategyforIntegration4837.6IntegrationUsingTablesandComputerAlgebraSystems489DiscoveryProjectNPatternsinIntegrals494765
vi||||CONTENTS7.7ApproximateIntegration4957.8ImproperIntegrals508Review518ProblemsPlus521FURTHERAPPLICATIONSOFINTEGRATION5248.1ArcLength525DiscoveryProjectNArcLengthContest5328.2AreaofaSurfaceofRevolution532DiscoveryProjectNRotatingonaSlant5388.3ApplicationstoPhysicsandEngineering539DiscoveryProjectNComplementaryCoffeeCups5508.4ApplicationstoEconomicsand
Biology5508.5Probability555Review562ProblemsPlus564DIFFERENTIALEQUATIONS5669.1ModelingwithDifferentialEquations5679.2DirectionFieldsandEuler’sMethod5729.3Separable
Equations580AppliedProjectNHowFastDoesaTankDrain?
588AppliedProjectNWhichIsFaster,GoingUporComingDown?
5909.4ModelsforPopulationGrowth591AppliedProjectNCalculusandBaseball6019.5LinearEquations6029.6Predator-PreySystems608Review614ProblemsPlus61898
PARAMETRICEQUATIONSANDPOLARCOORDINATES62010.1CurvesDefinedbyParametricEquations621LaboratoryProjectNRunningCirclesaroundCircles62910.2CalculuswithParametricCurves630LaboratoryProjectNBé
zierCurves63910.3PolarCoordinates63910.4AreasandLengthsinPolarCoordinates65010.5ConicSections65410.6ConicSectionsinPolarCoordinates662Review669ProblemsPlus672INFINITESEQUENCESAND
SERIES67411.1Sequences675LaboratoryProjectNLogisticSequences68711.2Series68711.3TheIntegralTestandEstimatesofSums69711.4TheComparisonTests70511.5Alternating文库
Series71011.6AbsoluteConvergenceandtheRatioandRootTests71411.7StrategyforTestingSeries72111.8PowerSeries72311.9RepresentationsofFunctionsasPowerSeries72811.10TaylorandMaclaurinSeries734LaboratoryProjectNAnElusiveLimit748WritingProjectNHowNewtonDiscoveredtheBinomialSeries74811.11ApplicationsofTaylorPolynomials749AppliedProjectNRadiationfromtheStars757Review758ProblemsPlus7611110CONTENTS||||vii
viii||||CONTENTSVECTORSANDTHEGEOMETRYOFSPACE76412.1Three-DimensionalCoordinateSystems76512.2Vectors77012.3TheDotProduct77912.4TheCrossProduct786DiscoveryProjectNTheGeometryofaTetrahedron79412.5EquationsofLinesandPlanes794LaboratoryProjectNPutting3DinPerspective80412.6CylindersandQuadricSurfaces804Review812ProblemsPlus815VECTORFUNCTIONS81613.1VectorFunctionsandSpaceCurves81713.2DerivativesandIntegralsofVectorFunctions82413.3ArcLengthandCurvature83013.4MotioninSpace:
VelocityandAcceleration838AppliedProjectNKepler’sLaws848Review849Problems
Plus852PARTIALDERIVATIVES85414.1FunctionsofSeveralVariables85514.2LimitsandContinuity87014.3PartialDerivatives87814.4TangentPlanesandLinear
Approximations89214.5TheChainRule90114.6DirectionalDerivativesandtheGradientVector91014.7MaximumandMinimumValues922AppliedProjectNDesigningaDumpster933DiscoveryProjectNQuadraticApproximationsandCriticalPoints933141312LONDONOPARIS
CONTENTS||||ix14.8LagrangeMultipliers934AppliedProjectNRocketScience941Applied
TurbineOptimization943Review944ProblemsPlus948MULTIPLEProjectNHydro-
INTEGRALS95015.1DoubleIntegralsoverRectangles95115.2IteratedIntegrals95915.3DoubleIntegralsoverGeneralRegions96515.4DoubleIntegralsinPolar
Coordinates97415.5ApplicationsofDoubleIntegrals98015.6TripleIntegrals990DiscoveryProjectNVolumesofHyperspheres100015.7TripleIntegralsinCylindricalCoordinates1000DiscoveryProjectNTheIntersectionofThreeCylinders100515.8TripleIntegralsinSphericalCoordinates1005AppliedProjectNRollerDerby101215.9ChangeofVariablesinMultipleIntegrals1012Review1021ProblemsPlus1024VECTORCALCULUS102616.1VectorFields102716.2LineIntegrals103416.3TheFundamentalTheoremforLine
Integrals104616.4Green’sTheorem105516.5CurlandDivergence106116.6ParametricSurfacesandTheirAreas107016.7SurfaceIntegrals108116.8Stokes’Theorem1092WritingProjectNThree
MenandTwoTheorems10981615
x||||CONTENTS16.9TheDivergenceTheorem109916.10Summary1105Review1106ProblemsPlus1109SECOND-ORDERDIFFERENTIALEQUATIONS111017.1Second-OrderLinear
Equations111117.2NonhomogeneousLinearEquations111717.3ApplicationsofSecond-OrderDifferentialEquations112517.4SeriesSolutions1133Review1137APPENDIXESA1ANumbers,Inequalities,andAbsoluteValuesA2BCoordinateGeometryandLinesA10CGraphsofSecond-DegreeEquationsA16DTrigonometryA24ESigmaNotationA34FProofsofTheoremsA39GTheLogarithmDefinedasanIntegralA50HComplexNumbersA57IAnswerstoOdd-NumberedExercisesA65INDEXA13117
xiAgreatdiscoverysolvesagreatproblembutthereisagrainofdiscoveryinthesolut
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