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目录第一部分英汉微积分词汇Part1English-ChineseCalculusVocabulary第一章函数与极限Chapter1functionandLimit………………………………………………1第二章导数与微分Chapter2DerivativeandDifferential………………………………………2第三章微分中值定理Chapter3MeanValuetheoremofdifferentialsandtheApplicationofDerivatives………………………………………3第四章不定积分Chapter4IndefiniteIntegrals………………………………………………3第五章定积分Chapter5DefiniteIntegral…………………………………………………3第六章定积分的应用Chapter6ApplicationoftheDefiniteIntegrals……………………………4第七章空间解析几何与向量代数Chapter7SpaceAnalyticGeometryandVectorAlgebra…………………4第八章多元函数微分法及其应用Chapter8DifferentiationoffunctionsSeveralvariablesandItsApplication………………………………………………5第九章重积分MultipleIntegrals………………………………………………6第十章曲线积分与曲面积分Chapter10Line(Curve)IntegralsandSurfaceIntegrals……………………6第十一章无穷级数Chapter11InfiniteSeries……………………………………………………6第十二章微分方程Chapter12DifferentialEquation……………………………………………7第二部分定理定义公式的英文表达Part2EnglishExpressionforTheorem,DefinitionandFormula第一章函数与极限Chapter1FunctionandLimit………………………………………………191.1映射与函数(MappingandFunction)………………………………191.2数列的极限(LimitoftheSequenceofNumber)……………………201.3函数的极限(LimitofFunction)……………………………………211.4无穷小与无穷大(InfinitesimalandInfinity)………………………231.5极限运算法则(OperationRuleofLimit)……………………………241.6极限存在准则两个重要的极限(RulefortheExistenceofLimitsTwoImportantLimits)…………………………251.7无穷小的比较(TheComparisonofinfinitesimal)……………………261.8函数的连续性与间断点(ContinuityofFunctionAndDiscontinuityPoints)……………………………………………281.9连续函数的运酸与初等函数的连续性(OperationOfContinuousFunctionsandContinuityofElementaryFunctions)…………………………………………………281.10闭区间上连续函数的性质(PropertiesofContinuousFunctionsonaClosedInterval)…………………………30第二章导数与数分Chapter2DerivativeandDifferential……………………………………………312.1导数的概念(TheConceptofDerivative)………………………………312.2函数的求导法则(RulesforFindingDerivatives)………………………332.3高阶导数(Higher-orderDerivatives)……………………………………342.4隐函数及由参数方程所确定的函数的导数相关变化率(DerivativesofImplicitFunctionsandFunctionsDeterminedbyParametricEquationandCorrelativeChangeRate)…342.5函数的微分(DifferentialofaFunction)………………………35第三章微分中值定理与导数的应用Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives………………………………………363.1微分中值定理(TheMeanValueTheorem)……………………………363.2洛必达法则(L’Hospital’sRule)……………………………………………383.3泰勒公式(Taylor’sFormula)……………………………………………413.4函数的单调性和曲线的凹凸性(MonotonicityofFunctionsandConcavityofCurves)…………………………………433.5函数的极值与最大最小值(Extrema,MaximaandMinimaofFunctions)……………………………………………463.6函数图形的描绘(GraphingFunctions)………………………………493.7曲率(Curvature)………………………………………………………503.8方程的近似解(SolvingEquationNumerically)………………………53第四章不定积分Chapter4IndefiniteIntegrals…………………………………………………544.1不定积分的概念与性质(TheConceptandPropertiesofIndefiniteIntegrals)………………………………………544.2换元积分法(SubstitutionRuleforIndefiniteIntegrals)………………564.3分部积分法(IntegrationbyParts)………………………………………574.4有理函数的积分(IntegrationofRationalFunctions)…………………58第五章定积分Chapter5DefiniteIntegrals…………………………………………………615.1定积分的概念和性质(ConceptofDefiniteIntegralanditsProperties)………………………………………………………615.2微积分基本定理(FundamentalTheoremofCalculus)………………675.3定积分的换元法和分部积分法(IntegrationbySubstitutionandDefiniteIntegralsbyParts)……………………………………………695.4反常积分(ImproperIntegrals)…………………………………………70第六章定积分的应用Chapter6ApplicationsoftheDefiniteIntegrals……………………………756.1定积分的元素法(TheElementMethodofDefiniteIntegra……………756.2定积分在几何学上的应用(ApplicationsoftheDefiniteIntegralstoGeometry)………………………………………………766.3定积分在物理学上的应用(ApplicationsoftheDefiniteIntegralstoPhysics)……………………………………………………79第七章空间解析几何与向量代数Chapter7SpaceAnalyticGeometryandVectorAlgebar……………………807.1向量及其线性运算(VectorandItsLinearOperation)…………………807.2数量积向量积(DotProductandCrossProduct)……………………867.3曲面及其方程(SurfaceandItsEquation)………………………………897.4空间曲线及其方程(TheCurveinThree-spaceandItsEquation………917.5平面及其方程（PlaneinSpaceandItsEquation)……………………937.6空间直线及其方程（LinesinandTheirEquations)……………………95第八章多元函数微分法及其应用Chapter8DifferentiationofFunctionsofSeveralVariablesandItsApplication………………………………………998.1多元函数的基本概念（TheBasicConceptsofFunctionsofSeveralVariables)………………………………………………………998.2偏导数(PartialDerivative)………………………………………………1028.3全微分(TotalDifferential)………………………………………………1038.4链式法则（TheChainRule)……………………………………………1048.5隐函数的求导公式(DerivativeFormulaforImplicitFunctions).………1048.6多元函数微分学的几何应用(GeometricApplicationsofDifferentiationofFfunctionsofSeveralvariables)……1068.7方向导数与梯度(DirectionalDerivativesandGradients)…………………1078.8多元函数的极值(ExtremeValueofFunctionsofSeveralVariables)……108第九章重积分Chapter9MultipleIntegrals……………………………………………………1119.1二重积分的概念与性质(TheConceptofDoubleIntegralsandItsProperities)…………………………………………………………1119.2二重积分的计算法(EvaluationofdoubleIntegrals)………………………1149.3三重积分(TripleIntegrals)…………………………………………………1159.4重积分的应用(ApplicationsofMultipleItegrals)………………………120第十章曲线积分与曲面积分Chapte10LineIntegralsandSurfaceIntegrals………………………………12110.1对弧长的曲线积分(lineIntergralswithRespecttoArcLength)………12110.2对坐标的曲线积分(LineIntegralswithrespecttoCoordinateVariables)……………………………………………………12310.3格林公式及其应用(Green'sFormulaandItsApplications)………………12410.4对面积的曲面积分(SurfaceIntegralswithRespecttoAarea)……………12610.5对坐标的曲面积分(SurfaceIntegralswithRespecttoCoordinateVariables)………………………………………………………12810.6高斯公式通量与散度(Gauss'sFormulaFluxandDivirgence)……13010.7斯托克斯公式环流量与旋度(Stokes'sFormulaCirculationandRot