英汉微积分词汇

第一部分英汉微积分词汇Part1English-ChineseCalculusVocabulary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(antiderivative)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反常积分improperintegral反常积分发散theimproperintegralisdivergent反常积分收敛theimproperintegralisconvergent无穷限的反常积分improperintegralonaninfiniteinterval无界函数的反常积分improperintegralofunboundedfunctions绝对收敛absolutelyconvergent第六章定积分的应用Chapter6ApplicationsoftheDefiniteIntegrals元素法theelementmethod面积元素elementofarea平面图形的面积areaofaluanefigure直角坐标又称“笛卡儿坐标(Cartesiancoordinates)”极坐标polarcoordinates抛物线parabola椭圆ellipse旋转体的面积volumeofasolidofrotation旋转椭球体ellipsoidofrevolution,ellipsoidofrotation曲线的弧长arclengthofacurve可求长的rectifiable光滑smooth功work水压力waterpressure引力gravitation变力variableforce第七章空间解析几何与向量代数Chapter7SpaceAnalyticGeometryandVectorAlgebra向量vector自由向量freevector单位向量unitvector零向量zerovector相等equal平行parallel向量的线性运算linearpoerationofvector三角法则trianglerule平行四边形法则parallelogramrule交换律commutativelaw结合律associativelaw负向量negativevector差difference分配律distributivelaw空间直角坐标系spacerectangularcoordinates坐标面coordinateplane卦限octant向量的模modulusofvector向量a与b的夹角anglebetweenvectoraandb方向余弦directioncosine方向角directionangle向量在轴上的投影projectionofavectorontoanaxis数量积，外积，叉积scalarproduct,dotproduct,innerproduct曲面方程equationforasurface球面sphere旋转曲面surfaceofrevolution母线generatingline轴axis圆锥面cone顶点vertex旋转单叶双曲面revolutionhyperboloidsofonesheet旋转双叶双曲面revolutionhyperboloidsoftwosheets柱面cylindricalsurface,cylinder圆柱面cylindricalsurface准线directrix抛物柱面paraboliccylinder二次曲面quadricsurface椭圆锥面dllipticcone椭球面ellipsoid单叶双曲面hyperboloidofonesheet双叶双曲面hyperboloidoftwosheets旋转椭球面ellipsoidofrevolution椭圆抛物面ellipticparaboloid旋转抛物面paraboloidofrevolution双曲抛物面hyperbolicparaboloid马鞍面saddlesurface椭圆柱面ellipticcylinder双曲柱面hyperboliccylinder抛物柱面paraboliccylinder空间曲线spacecurve空间曲线的一般方程generalformequationsofaspacecurve空间曲线的参数方程parametricequationsofaspacecurve螺转线spiral螺矩pitch投影柱面projectingcylinder投影projection平面的点法式方程pointnormformeqyationofaplane法向量normalvector平面的一般方程generalformequationofaplane两平面的夹角anglebetweentwoplanes点到平面的距离distancefromapointtoaplane空间直线的一般方程generalequationofalineinspace方向向量directionvector直线的点向式方程pointdirectionformequationsofaline方向数directionnumber直线的参数方程parametricequationsofaline两直线的夹角anglebetweentwolines垂直perpendicular直线与平面的夹角anglebetweenalineandaplanes平面束pencilofplanes平面束的方程equationofapencilofplanes行列式determinant系数行列式coefficientdeterminant第八章多元函数微分法及其应用Chapter8DifferentiationofFunctionsofSeveralVariablesandItsApplication一元函数functionofonevariable多元函数functionofseveralvariables内点interiorpoint外点exteriorpoint边界点frontierpoint,boundarypoint聚点pointofaccumulation开集openset闭集closedset连通集connectedset开区域openregion闭区域closedregion有界集boundedset无界集unboundedsetn维空间n-dimentionalspace二重极限doublelimit多元函数的连续性continuityoffunctionofseveal连续函数continuousfunction不连续点discontinuitypoint一致连续uniformlycontinuous偏导数partialderivative对自变量x的偏导数partialderivativewithrespecttoindependentvariablex高阶偏导数partialderivativeofhigherorder二阶偏导数secondorderpartialderivative混合偏导数hybridpartialderivative全微分totaldifferential偏增量oartialincrement偏微分partialdifferential全增量totalincrement可微分differentiable必要条件necessarycondition充分条件sufficientcondition叠加原理superpostitionprinciple全导数totalderivative中间变量intermediatevariable隐函数存在定理theoremoftheexistenceofimplicitfunction曲线的切向量tangentvectorofacurve法平面normalplane向量方程vectorequation向量值函数vector-valuedfunction切平面tangentplane法线normalline方向导数directionalderivative梯度gradient数量场scalarfield梯度场gradientfield向量场vectorfield势场potentialfield引力场gravitationalfield引力势gravitationalpotential曲面在一点的切平面tangentplanetoasurfaceatapoint曲线在一点的法线normallinetoasurfaceatapoint无条件极值unconditionalextremevalues条件极值conditionalextremevalues拉格朗日乘数法Lagrangemultipliermethod拉格朗日乘子Lagrangemultiplier经验公式empiricalformula最小二乘法methodofleastsquares均方误差meansquareerror重积分Chapter9MultipleIntegrals二重积分doubleintegral可加性additivity累次积分iteratedintegral体积元素volumeelement三重积分tripleintegral直角坐标系中的体积元素volumeelementinrectangularcoordinatesystem柱面坐标cylindricalcoordinates柱面坐标系中的体积元素volumeelementincylindricalcoordinatesystem球面坐标sphericalcoordinates球面坐标系中的体积元素volumeelementinsphericalcoordinatesystem反常二重积分improperdoubleintegral曲面的面积areaofasurface质心centreofmass静矩staticmoment密度density形心centroid转动惯量momentofinertia参变量parametricvariable曲线积分与曲面积分Chapter10Line(Curve)IntegralsandSurfaceIntegrals对弧长的曲线积分lineintegralswithrespecttoarchength第一类曲线积分lineintegralsofthefirsttype对坐标的曲线积分lineintegralswithrespecttox,y,andz第二类曲线积分lineintegralsofthesecondtype有向曲线弧directedarc单连通区域simpleconnectedregion复连通区域complexconnectedregion格林公式Greenformula第一类曲面积分surfaceintegralsofthefirsttype对面的曲面积分surfaceintegralswithrespecttoarea有向曲面directedsurface对坐标的曲面积分surfaceintegralswithrespecttocoordinateelements第二类曲面积分surfaceintegralsofthesecondtype有向曲面元elementofdirectedsurface高斯公式gaussformula拉普拉斯算子Laplaceoperator格林第一公式Green’sfirstformula通量flux散度divergence斯托克斯公式Stokesformula环流量circulation旋度rotation,curl无穷级数Chapter11InfiniteSeries一般项generalterm部分和partialsum余项remainderterm等比级数geometricseries几何级数geometricseries公比commonratio调和级数harmonicseries柯西收敛准则Cauchyconvergencecriteria,Cauchycriteriaforconvergence正项级数seriesofpositiveterms达朗贝尔判别法D’Alemberttest柯西判别法Cauchytest交错级数alternatingseries绝对收敛absolutelyconvergent条件收敛conditionallyconvergent柯西乘积Cauchyproduct函数项级数seriesoffunctions发散点pointofdivergence收敛点pointofconvergence收敛域convergencedomain和函数sumfunction幂级数powerseries幂级数的系数coeffcientsofpowerseries阿贝尔定理AbelTheorem收敛半径radiusofconvergence收敛区间intervalofconvergence泰勒级数Taylorseries麦克劳林级数Maclaurinseries二项展开式binomialexpansion近似计算approximatecalculation舍入误差round-offerror,roundingerror欧拉公式Euler’sformula魏尔斯特拉丝判别法Weierstrasstest三角级数trigonometricseries振幅amplitude角频率angularfrequency初相initialphase矩形波squarewave谐波分析harmonicanalysis直流分量directcomponent基波fundamentalwave二次谐波secondharmonic三角函数系trigonometricfunctionsystem傅立叶系数Fouriercoefficient傅立叶级数Forrierseries周期延拓periodicprolongation正弦级数sineseries余弦级数cosineseries奇延拓oddprolongation偶延拓evenprolongation傅立叶级数的复数形式complexformofFourierseries微分方程Chapter12DifferentialEquation解微分方程solveadirrerentialequation常微分方程ordinarydifferentialequation偏微分方程partialdifferentialequation,PDE微分方程的阶orderofadifferentialequation微分方程的解solutionofadifferentialequation微分方程的通解generalsolutionofadifferentialequation初始条件initialcondition微分方程的特解particularsolutionofadifferentialequation初值问题initialvalueproblem微分方程的积分曲线integralcurveofadifferentialequation可分离变量的微分方程variableseparabledifferentialequation隐式解implicitsolution隐式通解