the calculus bible

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1、Contents1Functions21.1TheConceptofaFunction....................21.2TrigonometricFunctions.....................121.3InverseTrigonometricFunctions.................191.4Logarithmic,ExponentialandHyperbolicFunctions......262LimitsandContinuity352.1Intuitivetreatmentanddefinitions...............352.

2、1.1IntroductoryExamples..................352.1.2Limit:FormalDefinitions................412.1.3Continuity:FormalDefinitions.............432.1.4ContinuityExamples...................482.2LinearFunctionApproximations.................612.3LimitsandSequences.......................722.4PropertiesofCont

3、inuousFunctions...............842.5LimitsandInfinity........................943Differentiation993.1TheDerivative..........................993.2TheChainRule..........................1113.3DifferentiationofInverseFunctions...............1183.4ImplicitDifferentiation......................1303.5Higher

4、OrderDerivatives.....................1374ApplicationsofDifferentiation1464.1MathematicalApplications....................1464.2Antidifferentiation........................1574.3LinearFirstOrderDifferentialEquations............164iiiCONTENTS4.4LinearSecondOrderHomogeneousDifferentialEquations...1694.

5、5LinearNon-HomogeneousSecondOrderDifferentialEquations1795TheDefiniteIntegral1835.1AreaApproximation.......................1835.2TheDefiniteIntegral.......................1925.3IntegrationbySubstitution....................2105.4IntegrationbyParts.......................2165.5Logarithmic,Exponentia

6、landHyperbolicFunctions......2305.6TheRiemannIntegral......................2425.7VolumesofRevolution......................2505.8ArcLengthandSurfaceArea..................2606TechniquesofIntegration2676.1Integrationbyformulae......................2676.2IntegrationbySubstitution..................

7、..2736.3IntegrationbyParts.......................2766.4TrigonometricIntegrals......................2806.5TrigonometricSubstitutions...................2826.6IntegrationbyPartialFractions.................2886.7FractionalPowerSubstitutions