内容简介

  《托马斯微积分》1951年出版第11版,是一本深受美国广大教师和学生欢迎的教材,不少学校和教师采用它作为微积分课程的教材,在相当一段时间里,它是麻省理工学院微积分课程所用的教材之一。
  韦尔、哈斯、吉尔当诺著的《托马斯微积分(影印版下第11版)(英文版)》具有以下几个突出特色:取材于科学和工程领域中的重要应用实例以及配置丰富的习题;对每个重要专题均用语言的、代数的、数值的、图像的方式予以陈述;重视数值计算和程序应用;切实融入数学建模和数学实验的思想和方法;每个新专题都通过清楚的、易于理解的例子启发式地引入,可读性强;配有丰富的教学资源,可用于教师教学和学生学习。

目录

Preface
Preliminaries
1.1RealNumbersandtheRealLine
1.2Lines,Circles,andParabolas
1.3FunctionsandTheirGraphs
1.4IdentifyingFunctions;MathematicalModels
1.5CombiningFunctions;ShiftingandScalingGraphs
1.6TrigonometricFunctions
1.7GraphingwithCalculatorsandComputers
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
LimitsandContinuity
2.1RatesofChangeandLimits
2.2CalculatingLimitsUsingtheLimitLaws
2.3ThePreciseDefinitionofaLimit91
2.4One-SidedLimitsandLimitsatInfinity
2.5InfiniteLimitsandVerticalAsymptotes
2.6Continuity
2.7TangentsandDerivatives
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
Differentiation
3.1TheDerivativeasaFunction
3.2DifferentiationRules
3.3TheDerivativeasaRateofChange
3.4DerivativesofTrigonometricFunctions
3.5TheChainRuleandParametricEquations
3.6ImplicitDifferentiation
3.7RelatedRates
3.8LinearizationandDifferentials
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
ApplicationsofDerivatives
4.1ExtremeValuesofFunctions
4.2TheMeanValueTheorem
4.3MonotonicFunctionsandtheFirstDerivativeTest
4.4ConcavityandCurveSketching
4.5AppliedOptimizationProblems
4.6IndeterminateFormsandUH6pital'sRule
4.7Newton'sMethod
4.8Antiderivatives
QUESTIONSTOGUIDEYOURREVmW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
Integration
5.1EstimatingwithFiniteSums
5.2SigmaNotationandLimitsofFiniteSums
5.3TheDefiniteIntegral
5.4TheFundamentalTheoremofCalculus
5.5IndefiniteIntegralsandtheSubstitutionRule
5.6SubstitutionandAreaBetweenCurves
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
ApplicationsofDefiniteIntegrals
6.1VolumesbySlicingandRotationAboutanAxis
6.2VolumesbyCylindricalShells
6.3LengthsofPlaneCurves
6.4MomentsandCentersofMass
6.5AreasofSurfacesofRevolutionandtheTheoremsofPappus
6.6Work447
6.7FluidPressuresandForces
QUESTIONSTOGUIDEYOURREVIEW461
PRACTICEEXERCISES461
ADDITIONALANDADVANCEDEXERCISES464
TranscendentalFunctions
7.1InverseFunctionsandTheirDerivatives
7.2NaturalLogarithms
7.3TheExponentialFunction
7.4axandlogax
7.5ExponentialGrowthandDecay
7.6RelativeRatesofGrowth
7.7InverseTrigonometricFunctions
7.8HyperbolicFunctions
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
TechniquesofIntegraUon
8.1BasicIntegrationFormulas
8.2IntegrationbyParts
8.3IntegrationofRationalFunctionsbyPartialFractions
8.4TrigonometricIntegrals
8.5TrigonometricSubstitutions
8.6IntegralTablesandComputerAlgebraSystems
8.7NumericalIntegration
8.8ImproperIntegrals
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
FurtherAppticationsofIntegration
9.1SlopeFieldsandSeparableDifferentialEquations
9.2First-OrderLinearDifferentialEquations
9.3Euler'sMethod
9.4GraphicalSolutionsofAutonomousDifferentialEquations
9.5ApplicationsofFirst-OrderDifferentialEquations
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
ConicSectionsandPotarCoordinates
10.1ConicSectionsandQuadraticEquations
10.2ClassifyingConicSectionsbyEccentricity
10.3QuadraticEquationsandRotations
10.4ConicsandParametricEquations;TheCycloid
10.5PolarCoordinates
10.6GraphinginPolarCoordinates
10.7AreasandLengthsinPolarCoordinates
10.8ConicSectionsinPolarCoordinates
QUESTIONSTOGUIDEYOURREWEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
InfiniteSequencesandSeries
11.1Sequences
11.2InfiniteSeries
11.3TheIntegralTest
11.4ComparisonTests
11.5TheRatioandRootTests
11.6AlternatingSeries,AbsoluteandConditionalConvergence
11.7PowerSeries
11.8TaylorandMaclaurinSeries
11.9ConvergenceofTaylorSeries;ErrorEstimates
11.10ApplicationsofPowerSeries
11.11FourierSeries
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
VectorsandtheGeometryofSpace
12.1Three-DimensionalCoordinateSystems
12.2Vectors
12.3TheDotProduct
12.4TheCrossProduct
12.5LinesandPlanesinSpace
12.6CylindersandQuadricSurfaces
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
Vector-ValuedFunctionsandMotioninSpace
13.1VectorFunctions906
13.2ModelingProjectileMotion920
13.3ArcLengthandtheUnitTangentVectorT
13.4CurvatureandtheUnitNormalVectorN
13.5TorsionandtheUnitBinormalVectorB
13.6PlanetaryMotionandSatellites
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
Part-iatDerivatives
14.1FunctionsofSeveralVariables___
14.2LimitsandContinuityinHigherDimensions
14.3PartialDerivatives
14.4TheChainRule
14.5DirectionalDerivativesandGradientVectors
14.6TangentPlanesandDifferentials
14.7ExtremeValuesandSaddlePoints
14.8LagrangeMultipliers
14.9PartialDerivativeswithConstrainedVariables
14.10Taylor'sFormulaforTwoVariables
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
MuttipteIntegrats
15.1DoubleIntegrals
15.2Areas,Moments,andCentersofMass
15.3DoubleIntegralsinPolarForm
15.4TripleIntegralsinRectangularCoordinates
15.5MassesandMomentsinThreeDimensions
15.6TripleIntegralsinCylindricalandSphericalCoordinates
15.7SubstitutionsinMultipleIntegrals
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES1138
ADDITIONALANDADVANCEDEXERCISES
IntegrationinVectorFields
16.1LineIntegrals
16.2VectorFields,Work,Circulation,andFlux
16.3PathIndependence,PotentialFunctions,andConservativeFields
16.4Green'sTheoreminthePlane
16.5SurfaceAreaandSurfaceIntegrals
16.6ParametrizedSurfaces
16.7Stokes'Theorem
16.8TheDivergenceTheoremandaUnifiedTheory
QUESTIONSTOGUIDEYOURREVIEW
PRACTICEEXERCISES
ADDITIONALANDADVANCEDEXERCISES
Appendices
A.1MathematicalInduction
A.2ProofsofLimitTheorems
A.3CommonlyOccurringLimits
A.4TheoryoftheRealNumbers
A.5ComplexNumbers
A.6TheDistributiveLawforVectorCrossProducts
A.7TheMixedDerivativeTheoremandtheIncrementTheorem
A.8TheAreaofaParallelogram'sProjectiononaPlane
A.9BasicAlgebra,Geometry,andTrigonometryFormulas
Answers
Index
ABriefTabteofIntegrats
Credits

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