托马斯微积分(上册)

托马斯微积分(上册)
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作者: [美]
出版社: 高等教育出版社
2004-07
版次: 1
ISBN: 9787040144246
定价: 45.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 606页
正文语种: 简体中文,英语
  •   《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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