托马斯微积分（上册）

图书标准信息

• 作者 [美]吉尔当诺、芬尼 著
• 出版社 高等教育出版社
• 出版时间 2004-07
• 版次 1
• ISBN 9787040144246
• 定价 45.00元
• 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

【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】

Preliminaries
1Lines1
2FunctionsandGraphs10
3ExponentialFunctions24
4InverseFunctionsandLogarithms31
5TrigonometricFunctionsandTheirlnverses44
6ParametricEquations60
7ModelingChange67
QUESTIONSTOGUIDEYOURREVIEW76
PRACTICEEXERCISES77
ADDITIONALEXERCISES：THEORY．EXAMPS．APPUCATIONS80
1LimitsandContinuity
1．1RatesofChangeandLimi85
1．2FindingLimiandOne-SidedLimits99
1．3LimiInvolvingInfinity112
1．4Continuity123
1．5TangentLines134
QUESTIONSTOGUIDEYOURREVIEW141
PRACTICEEXERCISES142
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS143
2DeriVatives
2．1TheDerivativeasaFunction147
2．2TheDerivativeasaRateofChange160
2．3DerivativesofProducts．Quotients．andNegativePowers173
2．4DerivativesofTrigonometricFunctions179
2．5TheChainRuleandParametricEquations187
2．6ImplicitDifierentiation198
2．7RelatedRates207
QUESTIONSTOGUIDEYOURREVIEW216
PRACTICEEXERCISES217
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS221
3ApplicationsofDerivatives
3．1ExtremeValuesofFunctions225
3．2TheMcanValueTheoremandDifierentialEquations237
3．3TheShapeofaGraph245
3．4GraphicalSolutionsofAutonomousDifferentialEquations257
3．5ModelingandOptimization266
3．6LinearizationandDifferentials283
3．7Newton’SMethod297
QUESTIONSTOGUIDEYOURREVIEW305
PRACTICEEXERCISES305
ADDITIONALEXERCISES：THEORY，EXAMPLES．APPLICATIONS309
4Integration
4．1IndefiniteIntegrals，DifferentialEquations．andModeling313
4．2IntegralRules；IntegrationbySubstitution322
4．3EstimatingwithFiniteSums329
4．4RicmannSumsandDefiniteIntegrals340
4．5TheMcanValueandFundamentaITheorems351
4．6SubStitutioninDefiniteIntegrals364
4．7NumericalIntegration373
QUESTIONSTOGUIDEYOURREVIEW384
PRACTICEEXERCISES385
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS389
5ApplicationsofIntegrals
5．1VolumesbySlicingandRotationAboutanAxis393
5．2ModelingVolumeUsingCylindricalShells406
5．3LengthsofPlaneCurves413
5．4Springs．Pumping．andLifting421
5．5FluidForces432
5．6MomentsandCentersofMass439
QUESTIONSTOGUIDEYOURREVIEW451
PRACTICEEXERCISES451
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS454
6TranscendentalFunctionsandDifferentialEquations
6．1Logarithms457
6．2ExponentialFunctions466
6．3D——e|rivativesofInverseTrigonometricFunctions；Integrals477
6．4First．OrderSeparableDifferentialEquations485
6．5LinearFirSt．OrderDifferentialEquations499
6．6Euler‘SMethod；PoplulationModels507
6．7HyperbolicFunctions520
QUESTIONSTOGUIDEYOURREVIEW530
PRACTICEEXERCISES531
ADDmONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS535
7IntegrationTechniques，LH6pital’sRule，andImproperIntegrals
7．1BasicIntegrationFormulas539
7．2IntegrationbyParts546
7．3PartialFractions555
7，4TrigonometricSubstitutions565
7．5IntegralTables．ComputerAlgebraSystems．and
MonteCarioIntegration570
7．6LHSpitarSRule578
7．7ImproperIntegrals586
QUESTIONSTOGUIDEYOURREVIEW600
PRACTICEEXERCISES601
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS603
8InfiniteSeries
8．1LimisofSequencesofNumbers608
8．2Subsequences．BoundedSequences．andPicardSMethod619
8．3InfiniteSeries627
8．4SeriesofNonnegativeTerms1639
8．5AlternatingSeries。AbsoluteandConditionalConvergence651
8．6PowerSeries660
8．7TaylorandMaclaurinSeries669
8．8ApplicationsofPowerSeries683
8．9FourierSeries691
8．10FourierCosineandSineSeries698
QUESTIONSTOGUIDEYOURREVIEW707
PRACTICEEXERCISES708
ADDITIONALEXERCISES：THEORY，EXAMPS．APPLICATIONS711
9VectorsinthePlaneandPolarFunctions
9．1VectorsinthePlane717
9．2DotProducts728
9．3Vector-ValuedFunctions738
9．4ModelingProjectileMotion749
9．5PolarCoordinatesandGraphs761
9．6CalculusofPolarCuryes770
QUESTIONSTOGUIDEYOURREVIEW780
PRACTICEEXERCISES780
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPUCATIONS784
10VectorsandM0tioninSpace
1O．1Cartesian(Rectangular)CoordinatesandVectorsinSpace787
10．2DotandCrossProducts796
10．3LinesandPlanesinSpace807
10．4cylindersandOuadricSurfaCes816
10．5Vector-ValuedFunctionsandSpaceCurves825
10．6ArcLengthandtheUnitTangentVectorT838
10．7TheTNBFrame；TangentialandNormalComponentsofAcceleration
10．8PlanetaryMotionandSatellites857
QUESTIONSTOGUIDEYOURREVIEW866
PRACTICEEXERCISES867
ADDITIONALEXERCISES：THEORY．EXAMPLES．APPLICATIONS870
11MultivariableFunctionsand111eirDerivatives
11．1FunctionsofSeveraIVariables873
11．2LimitsandContinuityinHigherDimensions882
11．3PartiaIDerivatives890
11．4TheChainRule902
11．5DirectionaIDerivatives．GradientVectors．andTangentPlanes911
11．6LinearizationandDifierentials925
11．7ExtremeValuesandSaddlePoints936
……
12MultipleIntegrals
13IntegrationinVectorFields
Appendices