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英汉微积分词汇English-ChineseCalculusVocabulary第一章函数与极限Chapter1FunctionandLimit高等数学highermathematics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象限quadrant原点origin坐标coordinate轴axisx轴x-axis整数integer有理数rationalnumber实数realnumber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centerofaneighborhood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absolutevalue绝对值函数absolutevaluefunction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最小上界leastupperbound无界unbounded函数的单调性monotonicityofafunction单调增加的increasing单调减少的decreasing严格递减strictlydecreasing严格递增strictlyincreasing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周期函数periodicfunction反函数inversefunction直接函数directfunction函数的复合compositionoffunction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线性函数linearfunction常数函数constantfunction多项式polynomial分段定义函数piecewisedefinedfunction阶梯函数stepfunction幂函数powerfunction指数函数exponentialfunction指数exponent自然指数函数naturalexponentialfunction对数logarithm对数函数logarithmicfunction自然对数函数naturallogarithmfunction三角函数trigonometricfunction正弦函数sinefunction余弦函数cosinefunction正切函数tangentfunction半角公式half-angleformulas反三角函数inversetrigonometricfunction常数函数constantfunction双曲线hyperbola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最优化问题optimizationproblems不等式inequality极限limit数列sequenceofnumber复利compoundinterest收敛convergence收敛的convergent收敛于aconvergetoa发散divergence发散的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limitoffunctionsasxapproaches0x单侧极限one-sidedlimit左极限leftlimit右极限rightlimit单侧极限one-sidedlimits渐近线asymptote水平渐近线horizontalasymptote分式fractions商定律quotientrule无穷小infinitesimal无穷大infinity铅直渐近线verticalasymptote夹逼准则squeezerule(Sandwichtheorem)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多项式的次数degreeofapolynomial三次函数cubicfunction函数的连续性continuityofafunction增量increment函数在x0连续thefunctioniscontinuousatx0左连续leftcontinuous/continuousfromtheleft右连续rightcontinuous/continuousfromtheright连续性continuity不连续性discontinuity连续函数continuousfunction函数在区间上连续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速率speed平均速度averagevelocity瞬时速度instantaneousvelocity匀速运动uniformmotion平均速度averagevelocity瞬时速度instantaneousvelocity圆的切线tangentlineofacircle割线secantline切线tangentline位置函数positionfunction导数derivative求导法differentiation可导的derivable可导函数differentiablefunction光滑曲线smoothcurve变化率rateofchange函数的变化率问题problemofthechangerateofafunction导函数derivedfunction导数定义域domainofderivative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]指数函数的导数derivativeofexponentialfunction幂函数的导数derivativeofpowerfunction切线的斜率slopeofthetangentline截距interceptsx截距x-intercept直线的斜截式slope-interceptequationofaline点斜式point-slopeform切线方程tangentequation焦点focus角速度angularvelocity成本函数costfunction边际成本marginalcost逐项求导法differentiationtermbyterm积之导数derivativeofaproduct商之导数derivativeofaquotient链式法则chainrule隐函数implicitfunction显函数explicitfunction隐函数求导法implicitdifferentiation加速度acceleration二阶导数secondderivative三阶导数thirdderivative高阶导数nthderivative/higherderivative莱布尼茨公式Leibnizformula对数求导法log-derivative参数parameter参数方程parametricequation相关变化率correlativechangerata微分differential微分学differential可微的differentiable函数的微分differentialoffunction自变量的微分differentialofindependentvariable微商differentialquotient逼近法approximation用微分逼近approximationbydifferentials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Chapter3MeanValueTheoremsofDifferentialsandtheApplicationofDerivatives均值定理meanvaluetheorem罗尔定理Roll’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’sRule不定式indetermi