Calculus (International Metric Edition)

Calculus (International Metric Edition)
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作者:
出版社: Cengage Learning
2011-01
版次: 7
ISBN: 9780538498845
定价: 680.60
装帧: 精装
开本: 其他
纸张: 其他
页数: 1368页
正文语种: 英语
2人买过
  • JamesStewart'sCALCULUStextsarewidelyrenownedfortheirmathematicalprecisionandaccuracy,clarityofexposition,andoutstandingexamplesandproblemsets.MillionsofstudentsworldwidehaveexploredcalculusthroughStewart'strademarkstyle,whileinstructorshaveturnedtohisapproachtimeandtimeagain.IntheSeventhEditionofCALCULUS,Stewartcontinuestosetthestandardforthecoursewhileaddingcarefullyrevisedcontent.Thepatientexplanations,superbexercises,focusonproblemsolving,andcarefullygradedproblemsetsthathavemadeStewart'stextsbest-sellerscontinuetoprovideastrongfoundationfortheSeventhEdition.Fromthemostunpreparedstudenttothemostmathematicallygifted,Stewart'swritingandpresentationservetoenhanceunderstandingandbuildconfidence. DiagnosticTests.
    APreviewofCalculus.
    1.FUNCTIONSANDLIMITS.
    FourWaystoRepresentaFunction.MathematicalModels:ACatalogofEssentialFunctions.NewFunctionsfromOldFunctions.TheTangentandVelocityProblems.TheLimitofaFunction.CalculatingLimitsUsingtheLimitLaws.ThePreciseDefinitionofaLimit.Continuity.Review.PrinciplesofProblemSolving.

    2.DERIVATIVES.
    DerivativesandRatesofChange.WritingProject:WritingProject:EarlyMethodsforFindingTangents.TheDerivativeasaFunction.DifferentiationFormulas.AppliedProject:BuildingaBetterRollerCoaster.DerivativesofTrigonometricFunctions.TheChainRule.AppliedProject:WhereShouldaPilotStartDescent?ImplicitDifferentiation.LaboratoryProject:FamiliesofImplicitCurves.RatesofChangeintheNaturalandSocialSciences.RelatedRates.LinearApproximationsandDifferentials.LaboratoryProject:TaylorPolynomials.Review.ProblemsPlus.

    3.APPLICATIONSOFDIFFERENTIATION.
    MaximumandMinimumValues.AppliedProject:TheCalculusofRainbows.TheMeanValueTheorem.HowDerivativesAffecttheShapeofaGraph.LimitsatInfinity;HorizontalAsymptotes.SummaryofCurveSketching.GraphingwithCalculusandCalculators.OptimizationProblems.AppliedProject:TheShapeofaCan.Newton'sMethod.Antiderivatives.Review.ProblemsPlus.

    4.INTEGRALS.
    AreasandDistances.TheDefiniteIntegral.DiscoveryProject:AreaFunctions.TheFundamentalTheoremofCalculus.IndefiniteIntegralsandtheNetChangeTheorem.WritingProject:Newton,Leibniz,andtheInventionofCalculus.TheSubstitutionRule.Review.ProblemsPlus.

    5.APPLICATIONSOFINTEGRATION.
    AreasBetweenCurves.AppliedProject:TheGiniIndex.Volume.VolumesbyCylindricalShells.Work.AverageValueofaFunction.Review.ProblemsPlus.

    6.INVERSEFUNCTIONS:EXPONENTIAL,LOGARITHMIC,ANDINVERSETRIGONOMETRICFUNCTIONS.
    InverseFunctions.InstructorsmaycovereitherSections6.2-6.4orSections6.2*-6.4*.SeethePreface.ExponentialFunctionsandTheirDerivatives.LogarithmicFunctions.DerivativesofLogarithmicFunctions.TheNaturalLogarithmicFunction.TheNaturalExponentialFunction.GeneralLogarithmicandExponentialFunctions.ExponentialGrowthandDecay.InverseTrigonometricFunctions.AppliedProject:WheretoSitattheMovies.HyperbolicFunctions.IndeterminateFormsandl'Hospital'sRule.WritingProject:TheOriginsofl'Hospital'sRule.Review.ProblemsPlus.

    7.TECHNIQUESOFINTEGRATION.
    IntegrationbyParts.TrigonometricIntegrals.TrigonometricSubstitution.IntegrationofRationalFunctionsbyPartialFractions.StrategyforIntegration.AppliedProject:CalculusandBaseball.IntegrationUsingTablesandComputerAlgebraSystems.DiscoveryProject:PatternsinIntegrals.ApproximateIntegration.ImproperIntegrals.Review.ProblemsPlus.

    8.FURTHERAPPLICATIONSOFINTEGRATION.
    ArcLength.DiscoveryProject:ArcLengthContest.AreaofaSurfaceofRevolution.DiscoveryProject:RotatingonaSlant.ApplicationstoPhysicsandEngineering.DiscoveryProject:ComplementaryCoffeeCups.ApplicationstoEconomicsandBiology.Probability.Review.ProblemsPlus.

    9.DIFFERENTIALEQUATIONS.
    ModelingwithDifferentialEquations.DirectionFieldsandEuler'sMethod.SeparableEquations.AppliedProject:HowFastDoesaTankDrain?AppliedProject:WhichisFaster,GoingUporComingDown?ModelsforPopulationGrowth.LinearEquations.Predator-PreySystems.Review.ProblemsPlus.

    10.PARAMETRICEQUATIONSANDPOLARCOORDINATES.
    CurvesDefinedbyParametricEquations.LaboratoryProject:FamiliesofHypocycloids.CalculuswithParametricCurves.LaboratoryProject:BézierCurves.PolarCoordinates.LaboratoryProject:FamiliesofPolarCurves.AreasandLengthsinPolarCoordinates.ConicSections.ConicSectionsinPolarCoordinates.Review.ProblemsPlus.

    11.INFINITESEQUENCESANDSERIES.
    Sequences.LaboratoryProject:LogisticSequences.Series.TheIntegralTestandEstimatesofSums.TheComparisonTests.AlternatingSeries.AbsoluteConvergenceandtheRatioandRootTests.StrategyforTestingSeries.PowerSeries.RepresentationsofFunctionsasPowerSeries.TaylorandMaclaurinSeries.LaboratoryProject:AnElusiveLimit.WritingProject:HowNewtonDiscoveredtheBinomialSeries.ApplicationsofTaylorPolynomials.AppliedProject:RadiationfromtheStars.Review.ProblemsPlus.

    12.VECTORSANDTHEGEOMETRYOFSPACE.
    Three-DimensionalCoordinateSystems.Vectors.TheDotProduct.TheCrossProduct.DiscoveryProject:TheGeometryofaTetrahedron.EquationsofLinesandPlanes.CylindersandQuadricSurfaces.Review.ProblemsPlus.

    13.VECTORFUNCTIONS.
    VectorFunctionsandSpaceCurves.DerivativesandIntegralsofVectorFunctions.ArcLengthandCurvature.MotioninSpace:VelocityandAcceleration.AppliedProject:Kepler'sLaws.Review.ProblemsPlus.

    14.PARTIALDERIVATIVES.
    FunctionsofSeveralVariables.LimitsandContinuity.PartialDerivatives.TangentPlanesandLinearApproximation.TheChainRule.DirectionalDerivativesandtheGradientVector.MaximumandMinimumValues.AppliedProject:DesigningaDumpster.DiscoveryProject:QuadraticApproximationsandCriticalPoints.LagrangeMultipliers.AppliedProject:RocketScience.AppliedProject:Hydro-TurbineOptimization.Review.ProblemsPlus.

    15.MULTIPLEINTEGRALS.
    DoubleIntegralsoverRectangles.IteratedIntegrals.DoubleIntegralsoverGeneralRegions.DoubleIntegralsinPolarCoordinates.ApplicationsofDoubleIntegrals.TripleIntegrals.DiscoveryProject:VolumesofHyperspheres.TripleIntegralsinCylindricalCoordinates.DiscoveryProject:TheIntersectionofThreeCylinders.TripleIntegralsinSphericalCoordinates.AppliedProject:RollerDerby.ChangeofVariablesinMultipleIntegrals.Review.ProblemsPlus.

    16.VECTORCALCULUS.
    VectorFields.LineIntegrals.TheFundamentalTheoremforLineIntegrals.Green'sTheorem.CurlandDivergence.ParametricSurfacesandTheirAreas.SurfaceIntegrals.Stokes'Theorem.WritingProject:ThreeMenandTwoTheorems.TheDivergenceTheorem.Summary.Review.ProblemsPlus.

    17.SECOND-ORDERDIFFERENTIALEQUATIONS.
    Second-OrderLinearEquations.NonhomogeneousLinearEquations.ApplicationsofSecond-OrderDifferentialEquations.SeriesSolutions.Review.ProblemsPlus.

    APPENDIXES.
    A.Intervals,Inequalities,andAbsoluteValues.
    B.CoordinateGeometryandLines.
    C.GraphsofSecond-DegreeEquations.
    D.Trigonometry.
    E.SigmaNotation.
    F.ProofsofTheorems.
    G.GraphingCalculatorsandComputers.
    H.ComplexNumbers.
    I.AnswerstoOdd-NumberedExercises.
  • 内容简介:
    JamesStewart'sCALCULUStextsarewidelyrenownedfortheirmathematicalprecisionandaccuracy,clarityofexposition,andoutstandingexamplesandproblemsets.MillionsofstudentsworldwidehaveexploredcalculusthroughStewart'strademarkstyle,whileinstructorshaveturnedtohisapproachtimeandtimeagain.IntheSeventhEditionofCALCULUS,Stewartcontinuestosetthestandardforthecoursewhileaddingcarefullyrevisedcontent.Thepatientexplanations,superbexercises,focusonproblemsolving,andcarefullygradedproblemsetsthathavemadeStewart'stextsbest-sellerscontinuetoprovideastrongfoundationfortheSeventhEdition.Fromthemostunpreparedstudenttothemostmathematicallygifted,Stewart'swritingandpresentationservetoenhanceunderstandingandbuildconfidence.
  • 目录:
    DiagnosticTests.
    APreviewofCalculus.
    1.FUNCTIONSANDLIMITS.
    FourWaystoRepresentaFunction.MathematicalModels:ACatalogofEssentialFunctions.NewFunctionsfromOldFunctions.TheTangentandVelocityProblems.TheLimitofaFunction.CalculatingLimitsUsingtheLimitLaws.ThePreciseDefinitionofaLimit.Continuity.Review.PrinciplesofProblemSolving.

    2.DERIVATIVES.
    DerivativesandRatesofChange.WritingProject:WritingProject:EarlyMethodsforFindingTangents.TheDerivativeasaFunction.DifferentiationFormulas.AppliedProject:BuildingaBetterRollerCoaster.DerivativesofTrigonometricFunctions.TheChainRule.AppliedProject:WhereShouldaPilotStartDescent?ImplicitDifferentiation.LaboratoryProject:FamiliesofImplicitCurves.RatesofChangeintheNaturalandSocialSciences.RelatedRates.LinearApproximationsandDifferentials.LaboratoryProject:TaylorPolynomials.Review.ProblemsPlus.

    3.APPLICATIONSOFDIFFERENTIATION.
    MaximumandMinimumValues.AppliedProject:TheCalculusofRainbows.TheMeanValueTheorem.HowDerivativesAffecttheShapeofaGraph.LimitsatInfinity;HorizontalAsymptotes.SummaryofCurveSketching.GraphingwithCalculusandCalculators.OptimizationProblems.AppliedProject:TheShapeofaCan.Newton'sMethod.Antiderivatives.Review.ProblemsPlus.

    4.INTEGRALS.
    AreasandDistances.TheDefiniteIntegral.DiscoveryProject:AreaFunctions.TheFundamentalTheoremofCalculus.IndefiniteIntegralsandtheNetChangeTheorem.WritingProject:Newton,Leibniz,andtheInventionofCalculus.TheSubstitutionRule.Review.ProblemsPlus.

    5.APPLICATIONSOFINTEGRATION.
    AreasBetweenCurves.AppliedProject:TheGiniIndex.Volume.VolumesbyCylindricalShells.Work.AverageValueofaFunction.Review.ProblemsPlus.

    6.INVERSEFUNCTIONS:EXPONENTIAL,LOGARITHMIC,ANDINVERSETRIGONOMETRICFUNCTIONS.
    InverseFunctions.InstructorsmaycovereitherSections6.2-6.4orSections6.2*-6.4*.SeethePreface.ExponentialFunctionsandTheirDerivatives.LogarithmicFunctions.DerivativesofLogarithmicFunctions.TheNaturalLogarithmicFunction.TheNaturalExponentialFunction.GeneralLogarithmicandExponentialFunctions.ExponentialGrowthandDecay.InverseTrigonometricFunctions.AppliedProject:WheretoSitattheMovies.HyperbolicFunctions.IndeterminateFormsandl'Hospital'sRule.WritingProject:TheOriginsofl'Hospital'sRule.Review.ProblemsPlus.

    7.TECHNIQUESOFINTEGRATION.
    IntegrationbyParts.TrigonometricIntegrals.TrigonometricSubstitution.IntegrationofRationalFunctionsbyPartialFractions.StrategyforIntegration.AppliedProject:CalculusandBaseball.IntegrationUsingTablesandComputerAlgebraSystems.DiscoveryProject:PatternsinIntegrals.ApproximateIntegration.ImproperIntegrals.Review.ProblemsPlus.

    8.FURTHERAPPLICATIONSOFINTEGRATION.
    ArcLength.DiscoveryProject:ArcLengthContest.AreaofaSurfaceofRevolution.DiscoveryProject:RotatingonaSlant.ApplicationstoPhysicsandEngineering.DiscoveryProject:ComplementaryCoffeeCups.ApplicationstoEconomicsandBiology.Probability.Review.ProblemsPlus.

    9.DIFFERENTIALEQUATIONS.
    ModelingwithDifferentialEquations.DirectionFieldsandEuler'sMethod.SeparableEquations.AppliedProject:HowFastDoesaTankDrain?AppliedProject:WhichisFaster,GoingUporComingDown?ModelsforPopulationGrowth.LinearEquations.Predator-PreySystems.Review.ProblemsPlus.

    10.PARAMETRICEQUATIONSANDPOLARCOORDINATES.
    CurvesDefinedbyParametricEquations.LaboratoryProject:FamiliesofHypocycloids.CalculuswithParametricCurves.LaboratoryProject:BézierCurves.PolarCoordinates.LaboratoryProject:FamiliesofPolarCurves.AreasandLengthsinPolarCoordinates.ConicSections.ConicSectionsinPolarCoordinates.Review.ProblemsPlus.

    11.INFINITESEQUENCESANDSERIES.
    Sequences.LaboratoryProject:LogisticSequences.Series.TheIntegralTestandEstimatesofSums.TheComparisonTests.AlternatingSeries.AbsoluteConvergenceandtheRatioandRootTests.StrategyforTestingSeries.PowerSeries.RepresentationsofFunctionsasPowerSeries.TaylorandMaclaurinSeries.LaboratoryProject:AnElusiveLimit.WritingProject:HowNewtonDiscoveredtheBinomialSeries.ApplicationsofTaylorPolynomials.AppliedProject:RadiationfromtheStars.Review.ProblemsPlus.

    12.VECTORSANDTHEGEOMETRYOFSPACE.
    Three-DimensionalCoordinateSystems.Vectors.TheDotProduct.TheCrossProduct.DiscoveryProject:TheGeometryofaTetrahedron.EquationsofLinesandPlanes.CylindersandQuadricSurfaces.Review.ProblemsPlus.

    13.VECTORFUNCTIONS.
    VectorFunctionsandSpaceCurves.DerivativesandIntegralsofVectorFunctions.ArcLengthandCurvature.MotioninSpace:VelocityandAcceleration.AppliedProject:Kepler'sLaws.Review.ProblemsPlus.

    14.PARTIALDERIVATIVES.
    FunctionsofSeveralVariables.LimitsandContinuity.PartialDerivatives.TangentPlanesandLinearApproximation.TheChainRule.DirectionalDerivativesandtheGradientVector.MaximumandMinimumValues.AppliedProject:DesigningaDumpster.DiscoveryProject:QuadraticApproximationsandCriticalPoints.LagrangeMultipliers.AppliedProject:RocketScience.AppliedProject:Hydro-TurbineOptimization.Review.ProblemsPlus.

    15.MULTIPLEINTEGRALS.
    DoubleIntegralsoverRectangles.IteratedIntegrals.DoubleIntegralsoverGeneralRegions.DoubleIntegralsinPolarCoordinates.ApplicationsofDoubleIntegrals.TripleIntegrals.DiscoveryProject:VolumesofHyperspheres.TripleIntegralsinCylindricalCoordinates.DiscoveryProject:TheIntersectionofThreeCylinders.TripleIntegralsinSphericalCoordinates.AppliedProject:RollerDerby.ChangeofVariablesinMultipleIntegrals.Review.ProblemsPlus.

    16.VECTORCALCULUS.
    VectorFields.LineIntegrals.TheFundamentalTheoremforLineIntegrals.Green'sTheorem.CurlandDivergence.ParametricSurfacesandTheirAreas.SurfaceIntegrals.Stokes'Theorem.WritingProject:ThreeMenandTwoTheorems.TheDivergenceTheorem.Summary.Review.ProblemsPlus.

    17.SECOND-ORDERDIFFERENTIALEQUATIONS.
    Second-OrderLinearEquations.NonhomogeneousLinearEquations.ApplicationsofSecond-OrderDifferentialEquations.SeriesSolutions.Review.ProblemsPlus.

    APPENDIXES.
    A.Intervals,Inequalities,andAbsoluteValues.
    B.CoordinateGeometryandLines.
    C.GraphsofSecond-DegreeEquations.
    D.Trigonometry.
    E.SigmaNotation.
    F.ProofsofTheorems.
    G.GraphingCalculatorsandComputers.
    H.ComplexNumbers.
    I.AnswerstoOdd-NumberedExercises.
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