高等数学名词(中英文).pdf

高等数学名词(中英文).pdf

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高高等数学等数学名词名词（中英文中英文）第一章第一章函数与极限函数与极限Chapter1FunctionandLimit集合set元素element子集subset空集emptyset并集union交集intersection差集differenceofset基本集basicset补集complementset直积directproduct笛卡儿积Cartesianproduct开区间openinterval闭区间closedinterval半开区间halfopeninterval有限区间finiteinterval区间的长度lengthofaninterval无限区间infiniteinterval领域neighborhood领域的中心centreofaneighborhood领域的半径radiusofaneighborhood左领域leftneighborhood右领域rightneighborhood映射mappingX到Y的映射mappingofXontoY满射surjection单射injection一一映射one-to-onemapping双射bijection算子operator变化transformation函数function逆映射inversemapping复合映射compositemapping自变量independentvariable因变量dependentvariable定义域domain函数值valueoffunction函数关系functionrelation值域range自然定义域naturaldomain单值函数singlevaluedfunction多值函数multiplevaluedfunction单值分支one-valuedbranch函数图形graphofafunction绝对值函数absolutevalue符号函数sighfunction整数部分integralpart阶梯曲线stepcurve当且仅当ifandonlyif（iff）分段函数piecewisefunction上界upperbound下界lowerbound有界boundedness无界unbounded函数的单调性monotonicityofafunction单调增加的increasing单调减少的decreasing单调函数monotonefunction函数的奇偶性parity（odevity）ofafunction对称symmetry偶函数evenfunction奇函数oddfunction函数的周期性periodicityofafunction周期period反函数inversefunction直接函数directfunction复合函数compositefunction中间变量intermediatevariable函数的运算operationoffunction基本初等函数basicelementaryfunction初等函数elementaryfunction幂函数powerfunction指数函数exponentialfunction对数函数logarithmicfunction三角函数trigonometricfunction反三角函数inversetrigonometricfunction常数函数constantfunction双曲函数hyperbolicfunction双曲正弦hyperbolicsine双曲余弦hyperboliccosine双曲正切hyperbolictangent反双曲正弦inversehyperbolicsine反双曲余弦inversehyperboliccosine反双曲正切inversehyperbolictangent极限limit数列sequenceofnumber收敛convergence收敛于aconvergetoa发散divergent极限的唯一性uniquenessoflimits收敛数列的有界性boundednessofaconvergentsequence子列subsequence函数的极限limitsoffunctions函数当x趋于x0时的极限limitoffunctionsasxapproachesx0左极限leftlimit右极限rightlimit单侧极限one-sidedlimits水平渐近线horizontalasymptote无穷小infinitesimal无穷大infinity铅直渐近线verticalasymptote夹逼准则squeezerule单调数列monotonicsequence高阶无穷小infinitesimalofhigherorder低阶无穷小infinitesimaloflowerorder同阶无穷小infinitesimalofthesameorder等阶无穷小equivalentinfinitesimal函数的连续性continuityofafunction增量increment函数在x0连续thefunctioniscontinuousatx0左连续leftcontinuous右连续rightcontinuous区间上的连续函数continuousfunction函数在该区间上连续functioniscontinuousonaninterval不连续点discontinuitypoint第一类间断点discontinuitypointofthefirstkind第二类间断点discontinuitypointofthesecondkind初等函数的连续性continuityoftheelementaryfunctions定义区间definedinterval最大值globalmaximumvalue（absolutemaximum）最小值globalminimumvalue（absoluteminimum）零点定理thezeropointtheorem介值定理intermediatevaluetheorem第二章第二章导数与微分导数与微分Chapter2DerivativeandDifferential速度velocity匀速运动uniformmotion平均速度averagevelocity瞬时速度instantaneousvelocity圆的切线tangentlineofacircle切线tangentline切线的斜率slopeofthetangentline位置函数positionfunction导数derivative可导derivable函数的变化率问题problemofthechangerateofafunction导函数derivedfunction左导数left-handderivative右导数right-handderivative单侧导数one-sidedderivatives在闭区间a,b上可导isderivableontheclosedintervala,b切线方程tangentequation角速度angularvelocity成本函数costfunction边际成本marginalcost链式法则chainrule隐函数implicitfunction显函数explicitfunction二阶函数secondderivative三阶导数thirdderivative高阶导数nthderivative莱布尼茨公式Leibnizformula对数求导法log-derivative参数方程parametricequation相关变化率correlativechangerata微分differential可微的differentiable函数的微分differentialoffunction自变量的微分differentialofindependentvariable微商differentialquotient间接测量误差indirectmeasurementerror绝对误差absoluteerror相对误差relativeerror第三章第三章微分中值定理与导数的应用微分中值定理与导数的应用Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives罗马定理Rollestheorem费马引理Fermatslemma拉格朗日中值定理Lagrangesmeanvaluetheorem驻点stationarypoint稳定点stablepoint临界点criticalpoint辅助函数auxiliaryfunction拉格朗日中值公式Lagrangesmeanvalueformula柯西中值定理Cauchysmeanvaluetheorem洛必达法则LHospitalsRule0/0型不定式indeterminateformoftype0/0不定式indeterminateform泰勒中值定理Taylorsmeanvaluetheorem泰勒公式Taylorformula余项remainderterm拉格朗日余项Lagrangeremainderterm麦克劳林公式Maclaurinsformula佩亚诺公式Peanoremainderterm凹凸性concavity凹向上的concaveupward,cancaveup凹向下的，向上凸的concavedownwardconcavedown拐点inflectionpoint函数的极值extremumoffunction极大值local（relative）maximum最大值global（absolute）mximum极小值local（relative）minimum最小值global（absolute）minimum目标函数objectivefunction曲率curvature弧微分arcdifferential平均曲率averagecurvature曲率园circleofcurvature曲率中心centerofcurvature曲率半径radiusofcurvature渐屈线evolute渐伸线involute根的隔离isolationofroot隔离区间isolationinterval切线法