高等数学名词(中英文)

高等数学名词(中英文)第一章函数与极限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isderivableontheclosedinterval[a,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第三章微分中值定理与导数的应用Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives罗马定理Rolle’stheorem费马引理Fermat’slemma拉格朗日中值定理Lagrange’smeanvaluetheorem驻点stationarypoint稳定点stablepoint临界点criticalpoint辅助函数auxiliaryfunction拉格朗日中值公式Lagrange’smeanvalueformula柯西中值定理Cauchy’smeanvaluetheorem洛必达法则L’Hospital’sRule0/0型不定式indeterminateformoftype0/0不定式indeterminateform泰勒中值定理Taylor’smeanvaluetheorem泰勒公式Taylorformula余项remainderterm拉格朗日余项Lagrangeremainderterm麦克劳林公式Maclaurin’sformula佩亚诺公式Peanoremainderterm凹凸性concavity凹向上的concaveupward,cancaveup凹向下的，向上凸的concavedownward’concavedown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tangentlinemethod第四章不定积分Chapter4IndefiniteIntegrals原函数primitivefunction(anti-derivative)积分号signofintegration被积函数integrand积分变量integralvariable积分曲线integralcurve积分表tableofintegrals换元积分法integrationbysubstitution分部积分法integrationbyparts分部积分公式formulaofintegrationbyparts有理函数rationalfunction真分式properfraction假分式improperfraction第五章定积分Chapter5DefiniteIntegrals曲边梯形trapezoidwith曲边curveedge窄矩形narrowrectangle曲边梯形的面积areaoftrapezoidwithcurvededge积分下限lowerlimitofintegral积分上限upperlimitofintegral积分区间integralinterval分割partition积分和integralsum可积integrable矩形法rectanglemethod积分中值定理meanvaluetheoremofintegrals函数在区间上的平均值averagevalueofafunctiononanintegvals牛顿－莱布尼茨公式Newton-Leibnizformula微积分基本公式fundamentalformulaofcalculus换元公式formulaforintegrationbysubstitution递推公式recurrenceformula反常