# 托马斯微积分（上册）

9.1

2004-07

ISBN: 9787040144246

• 　　《托马斯微积分》（上）（第10版影印版）从Pearson出版公司引进，是一本颇具影响的教材。50多年来，该书平均每4至5年就有一个新版面世，每版较之先前版本都有不少改进之处，体现了这是一部锐意革新的教材；与此同时，该书的一些基本特色始终注意保持且有所增强，说明它又是一部重视继承传统的教材。 Preliminaries1Lines12FunctionsandGraphs103ExponentialFunctions244InverseFunctionsandLogarithms315TrigonometricFunctionsandTheirlnverses446ParametricEquations607ModelingChange67QUESTIONSTOGUIDEYOURREVIEW76PRACTICEEXERCISES77ADDITIONALEXERCISES：THEORY．EXAMPS．APPUCATIONS801LimitsandContinuity1．1RatesofChangeandLimi851．2FindingLimiandOne-SidedLimits991．3LimiInvolvingInfinity1121．4Continuity1231．5TangentLines134QUESTIONSTOGUIDEYOURREVIEW141PRACTICEEXERCISES142ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS1432DeriVatives2．1TheDerivativeasaFunction1472．2TheDerivativeasaRateofChange1602．3DerivativesofProducts．Quotients．andNegativePowers1732．4DerivativesofTrigonometricFunctions1792．5TheChainRuleandParametricEquations1872．6ImplicitDifierentiation1982．7RelatedRates207QUESTIONSTOGUIDEYOURREVIEW216PRACTICEEXERCISES217ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS2213ApplicationsofDerivatives3．1ExtremeValuesofFunctions2253．2TheMcanValueTheoremandDifierentialEquations2373．3TheShapeofaGraph2453．4GraphicalSolutionsofAutonomousDifferentialEquations2573．5ModelingandOptimization2663．6LinearizationandDifferentials2833．7Newton’SMethod297QUESTIONSTOGUIDEYOURREVIEW305PRACTICEEXERCISES305ADDITIONALEXERCISES：THEORY，EXAMPLES．APPLICATIONS3094Integration4．1IndefiniteIntegrals，DifferentialEquations．andModeling3134．2IntegralRules；IntegrationbySubstitution3224．3EstimatingwithFiniteSums3294．4RicmannSumsandDefiniteIntegrals3404．5TheMcanValueandFundamentaITheorems3514．6SubStitutioninDefiniteIntegrals3644．7NumericalIntegration373QUESTIONSTOGUIDEYOURREVIEW384PRACTICEEXERCISES385ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS3895ApplicationsofIntegrals5．1VolumesbySlicingandRotationAboutanAxis3935．2ModelingVolumeUsingCylindricalShells4065．3LengthsofPlaneCurves4135．4Springs．Pumping．andLifting4215．5FluidForces4325．6MomentsandCentersofMass439QUESTIONSTOGUIDEYOURREVIEW451PRACTICEEXERCISES451ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS4546TranscendentalFunctionsandDifferentialEquations6．1Logarithms4576．2ExponentialFunctions4666．3D——e|rivativesofInverseTrigonometricFunctions；Integrals4776．4First．OrderSeparableDifferentialEquations4856．5LinearFirSt．OrderDifferentialEquations4996．6Euler‘SMethod；PoplulationModels5076．7HyperbolicFunctions520QUESTIONSTOGUIDEYOURREVIEW530PRACTICEEXERCISES531ADDmONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS5357IntegrationTechniques，LH6pital’sRule，andImproperIntegrals7．1BasicIntegrationFormulas5397．2IntegrationbyParts5467．3PartialFractions5557，4TrigonometricSubstitutions5657．5IntegralTables．ComputerAlgebraSystems．andMonteCarioIntegration5707．6LHSpitarSRule5787．7ImproperIntegrals586QUESTIONSTOGUIDEYOURREVIEW600PRACTICEEXERCISES601ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS6038InfiniteSeries8．1LimisofSequencesofNumbers6088．2Subsequences．BoundedSequences．andPicardSMethod6198．3InfiniteSeries6278．4SeriesofNonnegativeTerms16398．5AlternatingSeries。AbsoluteandConditionalConvergence6518．6PowerSeries6608．7TaylorandMaclaurinSeries6698．8ApplicationsofPowerSeries6838．9FourierSeries6918．10FourierCosineandSineSeries698QUESTIONSTOGUIDEYOURREVIEW707PRACTICEEXERCISES708ADDITIONALEXERCISES：THEORY，EXAMPS．APPLICATIONS7119VectorsinthePlaneandPolarFunctions9．1VectorsinthePlane7179．2DotProducts7289．3Vector-ValuedFunctions7389．4ModelingProjectileMotion7499．5PolarCoordinatesandGraphs7619．6CalculusofPolarCuryes770QUESTIONSTOGUIDEYOURREVIEW780PRACTICEEXERCISES780ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS78410VectorsandM0tioninSpace1O．1Cartesian(Rectangular)CoordinatesandVectorsinSpace78710．2DotandCrossProducts79610．3LinesandPlanesinSpace80710．4cylindersandOuadricSurfaCes81610．5Vector-ValuedFunctionsandSpaceCurves82510．6ArcLengthandtheUnitTangentVectorT83810．7TheTNBFrame；TangentialandNormalComponentsofAcceleration10．8PlanetaryMotionandSatellites857QUESTIONSTOGUIDEYOURREVIEW866PRACTICEEXERCISES867ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS87011MultivariableFunctionsand111eirDerivatives11．1FunctionsofSeveraIVariables87311．2LimitsandContinuityinHigherDimensions88211．3PartiaIDerivatives89011．4TheChainRule90211．5DirectionaIDerivatives．GradientVectors．andTangentPlanes91111．6LinearizationandDifierentials92511．7ExtremeValuesandSaddlePoints936……12MultipleIntegrals13IntegrationinVectorFieldsAppendices
• ##### 内容简介:
《托马斯微积分》（上）（第10版影印版）从Pearson出版公司引进，是一本颇具影响的教材。50多年来，该书平均每4至5年就有一个新版面世，每版较之先前版本都有不少改进之处，体现了这是一部锐意革新的教材；与此同时，该书的一些基本特色始终注意保持且有所增强，说明它又是一部重视继承传统的教材。
• ##### 目录:
Preliminaries1Lines12FunctionsandGraphs103ExponentialFunctions244InverseFunctionsandLogarithms315TrigonometricFunctionsandTheirlnverses446ParametricEquations607ModelingChange67QUESTIONSTOGUIDEYOURREVIEW76PRACTICEEXERCISES77ADDITIONALEXERCISES：THEORY．EXAMPS．APPUCATIONS801LimitsandContinuity1．1RatesofChangeandLimi851．2FindingLimiandOne-SidedLimits991．3LimiInvolvingInfinity1121．4Continuity1231．5TangentLines134QUESTIONSTOGUIDEYOURREVIEW141PRACTICEEXERCISES142ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS1432DeriVatives2．1TheDerivativeasaFunction1472．2TheDerivativeasaRateofChange1602．3DerivativesofProducts．Quotients．andNegativePowers1732．4DerivativesofTrigonometricFunctions1792．5TheChainRuleandParametricEquations1872．6ImplicitDifierentiation1982．7RelatedRates207QUESTIONSTOGUIDEYOURREVIEW216PRACTICEEXERCISES217ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS2213ApplicationsofDerivatives3．1ExtremeValuesofFunctions2253．2TheMcanValueTheoremandDifierentialEquations2373．3TheShapeofaGraph2453．4GraphicalSolutionsofAutonomousDifferentialEquations2573．5ModelingandOptimization2663．6LinearizationandDifferentials2833．7Newton’SMethod297QUESTIONSTOGUIDEYOURREVIEW305PRACTICEEXERCISES305ADDITIONALEXERCISES：THEORY，EXAMPLES．APPLICATIONS3094Integration4．1IndefiniteIntegrals，DifferentialEquations．andModeling3134．2IntegralRules；IntegrationbySubstitution3224．3EstimatingwithFiniteSums3294．4RicmannSumsandDefiniteIntegrals3404．5TheMcanValueandFundamentaITheorems3514．6SubStitutioninDefiniteIntegrals3644．7NumericalIntegration373QUESTIONSTOGUIDEYOURREVIEW384PRACTICEEXERCISES385ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS3895ApplicationsofIntegrals5．1VolumesbySlicingandRotationAboutanAxis3935．2ModelingVolumeUsingCylindricalShells4065．3LengthsofPlaneCurves4135．4Springs．Pumping．andLifting4215．5FluidForces4325．6MomentsandCentersofMass439QUESTIONSTOGUIDEYOURREVIEW451PRACTICEEXERCISES451ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS4546TranscendentalFunctionsandDifferentialEquations6．1Logarithms4576．2ExponentialFunctions4666．3D——e|rivativesofInverseTrigonometricFunctions；Integrals4776．4First．OrderSeparableDifferentialEquations4856．5LinearFirSt．OrderDifferentialEquations4996．6Euler‘SMethod；PoplulationModels5076．7HyperbolicFunctions520QUESTIONSTOGUIDEYOURREVIEW530PRACTICEEXERCISES531ADDmONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS5357IntegrationTechniques，LH6pital’sRule，andImproperIntegrals7．1BasicIntegrationFormulas5397．2IntegrationbyParts5467．3PartialFractions5557，4TrigonometricSubstitutions5657．5IntegralTables．ComputerAlgebraSystems．andMonteCarioIntegration5707．6LHSpitarSRule5787．7ImproperIntegrals586QUESTIONSTOGUIDEYOURREVIEW600PRACTICEEXERCISES601ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS6038InfiniteSeries8．1LimisofSequencesofNumbers6088．2Subsequences．BoundedSequences．andPicardSMethod6198．3InfiniteSeries6278．4SeriesofNonnegativeTerms16398．5AlternatingSeries。AbsoluteandConditionalConvergence6518．6PowerSeries6608．7TaylorandMaclaurinSeries6698．8ApplicationsofPowerSeries6838．9FourierSeries6918．10FourierCosineandSineSeries698QUESTIONSTOGUIDEYOURREVIEW707PRACTICEEXERCISES708ADDITIONALEXERCISES：THEORY，EXAMPS．APPLICATIONS7119VectorsinthePlaneandPolarFunctions9．1VectorsinthePlane7179．2DotProducts7289．3Vector-ValuedFunctions7389．4ModelingProjectileMotion7499．5PolarCoordinatesandGraphs7619．6CalculusofPolarCuryes770QUESTIONSTOGUIDEYOURREVIEW780PRACTICEEXERCISES780ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS78410VectorsandM0tioninSpace1O．1Cartesian(Rectangular)CoordinatesandVectorsinSpace78710．2DotandCrossProducts79610．3LinesandPlanesinSpace80710．4cylindersandOuadricSurfaCes81610．5Vector-ValuedFunctionsandSpaceCurves82510．6ArcLengthandtheUnitTangentVectorT83810．7TheTNBFrame；TangentialandNormalComponentsofAcceleration10．8PlanetaryMotionandSatellites857QUESTIONSTOGUIDEYOURREVIEW866PRACTICEEXERCISES867ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS87011MultivariableFunctionsand111eirDerivatives11．1FunctionsofSeveraIVariables87311．2LimitsandContinuityinHigherDimensions88211．3PartiaIDerivatives89011．4TheChainRule90211．5DirectionaIDerivatives．GradientVectors．andTangentPlanes91111．6LinearizationandDifierentials92511．7ExtremeValuesandSaddlePoints936……12MultipleIntegrals13IntegrationinVectorFieldsAppendices

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