微积分英文词汇,高数名词中英文对照,高等数学术语英语翻译一览

关键词:微积分英文,高等数学英文翻译,高数英语词汇来源:上海外教网|发布日期:2008-05-1617:12V、X、Z:Valueoffunction:函数值Variable:变数Vector:向量Velocity:速度Verticalasymptote:垂直渐近线Volume:体积X-axis:x轴x-coordinate:x坐标x-intercept:x截距Zerovector:函数的零点Zerosofapolynomial:多项式的零点T:Tangentfunction:正切函数Tangentline:切线Tangentplane:切平面Tangentvector:切向量Totaldifferential:全微分Trigonometricfunction:三角函数Trigonometricintegrals:三角积分Trigonometricsubstitutions:三角代换法Tripeintegrals:三重积分S:Saddlepoint:鞍点Scalar:纯量Secantline:割线Secondderivative:二阶导数SecondDerivativeTest:二阶导数试验法Secondpartialderivative:二阶偏导数Sector:扇形Sequence:数列Series:级数Set:集合Shellmethod:剥壳法Sinefunction:正弦函数Singularity:奇点Slantasymptote:斜渐近线Slope:斜率Slope-interceptequationofaline:直线的斜截式Smoothcurve:平滑曲线Smoothsurface:平滑曲面Solidofrevolution:旋转体Space:空间Speed:速率Sphericalcoordinates:球面坐标SqueezeTheorem:夹挤定理Stepfunction:阶梯函数Strictlydecreasing:严格递减Strictlyincreasing:严格递增Sum:和Surface:曲面Surfaceintegral:面积分Surfaceofrevolution:旋转曲面Symmetry:对称R:Radiusofconvergence:收敛半径Rangeofafunction:函数的值域Rateofchange:变化率Rationalfunction:有理函数Rationalizingsubstitution:有理代换法Rationalnumber:有理数Realnumber:实数Rectangularcoordinates:直角坐标Rectangularcoordinatesystem:直角坐标系Relativemaximumandminimum:相对极大值与极小值Revenuefunction:收入函数Revolution,solidof:旋转体Revolution,surfaceof:旋转曲面RiemannSum:黎曼和Riemanniangeometry:黎曼几何Right-handderivative:右导数Right-handlimit:右极限Root:根P、Q:Parabola:拋物线Paraboliccylinder:抛物柱面Paraboloid:抛物面Parallelepiped:平行六面体Parallellines:并行线Parameter:参数Partialderivative:偏导数Partialdifferentialequation:偏微分方程Partialfractions:部分分式Partialintegration:部分积分Partiton:分割Period:周期Periodicfunction:周期函数Perpendicularlines:垂直线Piecewisedefinedfunction:分段定义函数Plane:平面Pointofinflection:反曲点Polaraxis:极轴Polarcoordinate:极坐标Polarequation:极方程式Pole:极点Polynomial:多项式Positiveangle:正角Point-slopeform:点斜式Powerfunction:幂函数Product:积Quadrant:象限QuotientLawoflimit:极限的商定律QuotientRule:商定律M、N、O:Maximumandminimumvalues:极大与极小值MeanValueTheorem:均值定理Multipleintegrals:重积分Multiplier:乘子Naturalexponentialfunction:自然指数函数Naturallogarithmfunction:自然对数函数Naturalnumber:自然数Normalline:法线Normalvector:法向量Number:数Octant:卦限Oddfunction:奇函数One-sidedlimit:单边极限Openinterval:开区间Optimizationproblems:最佳化问题Order:阶Ordinarydifferentialequation:常微分方程Origin:原点Orthogonal:正交的L:Laplacetransform:Leplace变换LawofCosines:余弦定理Leastupperbound:最小上界Left-handderivative:左导数Left-handlimit:左极限Lemniscate:双钮线Length:长度Levelcurve:等高线L'Hospital'srule:洛必达法则Limacon:蚶线Limit:极限Linearapproximation:线性近似Linearequation:线性方程式Linearfunction:线性函数Linearity:线性Linearization:线性化Lineintheplane:平面上之直线Lineinspace:空间之直线Lobachevskigeometry:罗巴切夫斯基几何Localextremum:局部极值Localmaximumandminimum:局部极大值与极小值Logarithm:对数Logarithmicfunction:对数函数I:Implicitdifferentiation:隐求导法Implicitfunction:隐函数Improperintegral:瑕积分Increasing/DecreasingTest:递增或递减试验法Increment:增量IncreasingFunction:增函数Indefiniteintegral:不定积分Independentvariable:自变数Indeterminatefrom:不定型Inequality:不等式Infinitepoint:无穷极限Infiniteseries:无穷级数Inflectionpoint:反曲点Instantaneousvelocity:瞬时速度Integer:整数Integral:积分Integrand:被积分式Integration:积分Integrationbypart:分部积分法Intercepts:截距IntermediatevalueofTheorem:中间值定理Interval:区间Inversefunction:反函数Inversetrigonometricfunction:反三角函数Iteratedintegral:逐次积分H:Highermathematics高等数学/高数E、F、G、H:Ellipse:椭圆Ellipsoid:椭圆体Epicycloid:外摆线Equation:方程式Evenfunction:偶函数ExpectedValued:期望值ExponentialFunction:指数函数Exponents,lawsof:指数率Extremevalue:极值ExtremeValueTheorem:极值定理Factorial:阶乘FirstDerivativeTest:一阶导数试验法Firstoctant:第一卦限Focus:焦点Fractions:分式Function:函数FundamentalTheoremofCalculus:微积分基本定理Geometricseries:几何级数Gradient:梯度Graph:图形GreenFormula:格林公式Half-angleformulas:半角公式Harmonicseries:调和级数Helix:螺旋线HigherDerivative:高阶导数Horizontalasymptote:水平渐近线Horizontalline:水平线Hyperbola:双曲线Hyperboloid:双曲面D:Decreasingfunction:递减函数Decreasingsequence:递减数列Definiteintegral:定积分Degreeofapolynomial:多项式之次数Density:密度Derivative:导数ofacompositefunction:复合函数之导数ofaconstantfunction:常数函数之导数directional:方向导数domainof:导数之定义域ofexponentialfunction:指数函数之导数higher:高阶导数partial:偏导数ofapowerfunction:幂函数之导数ofapowerseries:羃级数之导数ofaproduct:积之导数ofaquotient:商之导数asarateofchange:导数当作变率right-hand:右导数second:二阶导数astheslopeofatangent:导数看成切线之斜率Determinant:行列式Differentiablefunction:可导函数Differential:微分Differentialequation:微分方程partial:偏微分方程Differentiation:求导法implicit:隐求导法partial:偏微分法termbyterm:逐项求导法Directionalderivatives:方向导数Discontinuity:不连续性Diskmethod:圆盘法Distance:距离Divergence:发散Domain:定义域Dotproduct:点积Doubleintegral:二重积分changeofvariablein:二重积分之变数变换inpolarcoordinates:极坐标二重积分C:Calculus:微积分differential:微分学integral:积分学Cartesiancoordinates:笛卡儿坐标一般指直角坐标Cartesiancoordinatessystem:笛卡儿坐标系Cauch'sMeanValueTheorem:柯西均值定理ChainRule:连锁律Changeofvariables:变数变换Circle:圆Circularcylinder:圆柱Closedinterval:封闭区间Coefficient:系数Compositionoffunction:函数之合成Compoundinterest:复利Concavity:凹性Conchoid:蚌线Cone:圆锥Constantfunction:常数函数Constantofintegration:积分常数Continuity:连续性atapoint:在一点处之连续性ofafunction:函数之连续性onaninterval:在区间之连续性fromtheleft:左连续fromtheright:右连续Continuousfunction:连续函数Convergence:收敛intervalof:收敛区间radiusof:收敛半径Convergentsequence:收敛数列series:收敛级数Coordinate:s:坐标Cartesian:笛卡儿坐标cylindrical:柱面坐标polar:极坐标rectangular:直角坐标spherical:球面坐标Coordinateaxes:坐标轴Coordinateplanes:坐标平面Cosinefunction:余弦函数Criticalpoint:临界点Cubicfunction:三次函数Curve:曲线Cylinder:圆柱CylindricalCoordinates:圆柱坐标A、B:Absoluteconvergence:绝对收敛Absoluteextremevalues:绝对极值Absolutemaximumandminimum:绝对极大与极小Absolutevalue:绝对值Absolutevaluefunction:绝对值函数Acceleration:加速度Antiderivative:反导数Approximateintegration:近似积分Approximation:逼近法bydifferentials:用微分逼近linear:线性逼近法bySimpson'sRule:Simpson法则逼近法bytheTrapezoidalRule:梯形法则逼近法Arbitraryconstant:任意常数Arclength:弧长Area:面积underacurve:曲线下方之面积betweencurves:曲线间之面积inpolarcoordinates:极坐标表示之面积ofasectorofacircle:扇形之面积ofasurfaceofarevolution:旋转曲面之面积Asymptote:渐近线horizontal:水平渐近线slant:斜渐近线vertical:垂直渐近线Averagespeed:平均速率Averagevelocity:平均速度Axes,coordinate:坐标轴Axesofellipse:椭圆之轴Binomialseries:二项级数微积分词汇第一章函数与极限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作者:新少年特工2007-10-818:37回复此发言2高等数学-翻译等阶无穷小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第九章重积分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第十章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第十一章无穷级数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第十二章微分方程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inplicitgeneralsolution衰变系数decaycoefficient衰变decay齐次方程homogeneousequation一阶线性方程lineardifferentialequationoffirstorder非齐次non-homogeneous齐次线性方程homogeneouslinearequation非齐次线性方程non-homogeneouslinearequation常数变易法methodofvariationofconstant暂态电流transientstatacurrent稳态电流steadystatecurrent伯努利方程Bernoulliequation全微分方程totaldifferentialequation积分因子integratingfactor高阶微分方程differentialequationofhigherorder悬链线catenary高阶线性微分方程lineradifferentialequationofhigherorder自由振动的微分方程differentialequationoffreevibration强迫振动的微分方程differentialequationofforcedoscillation串联电路的振荡方程oscillationequationofseriescircuit二阶线性微分方程secondorderlineradifferentialequation线性相关linearlydependence线性无关linearlyindependce二阶常系数齐次线性微分方程secondorderhomogeneourlineardifferentialequationwithconstantcoefficient二阶变系数齐次线性微分方程secondorderhomogeneouslineardifferentialequationwithvariablecoefficient特征方程characteristicequation无阻尼自由振动的微分方程differentialequationoffreevibrationwithzerodamping固有频率naturalfrequency简谐振动simpleharmonicoscillation,simpleharmonicvibration微分算子differentialoperator待定系数法methodofundeterminedcoefficient共振现象resonancephenomenon欧拉方程Eulerequation幂级数解法powerseriessolution数值解法numerialsolution勒让德方程Legendreequation微分方程组systemofdifferentialequations常系数线性微分方程组systemoflineradifferentialequationswithconstantcoefficientV、X、Z:Valueoffunction:函数值Variable:变数Vector:向量Velocity:速度Verticalasymptote:垂直渐近线Volume:体积X-axis:x轴x-coordinate:x坐标x-intercept:x截距Zerovector:函数的零点Zerosofapolynomial:多项式的零点T:Tangentfunction:正切函数Tangentline:切线Tangentplane:切平面Tangentvector:切向量Totaldifferential:全微分Trigonometricfunction:三角函数Trigonometricintegrals:三角积分Trigonometricsubstitutions:三角代换法Tripeintegrals:三重积分S:Saddlepoint:鞍点Scalar:纯量Secantline:割线Secondderivative:二阶导数SecondDerivativeTest:二阶导数试验法Secondpartialderivative:二阶偏导数Sector:扇形Sequence:数列Series:级数Set:集合Shellmethod:剥壳法Sinefunction:正弦函数Singularity:奇点Slantasymptote:斜渐近线Slope:斜率Slope-interceptequationofaline:直线的斜截式Smoothcurve:平滑曲线Smoothsurface:平滑曲面Solidofrevolution:旋转体Space:空间Speed:速率Sphericalcoordinates:球面坐标SqueezeTheorem:夹挤定理Stepfunction:阶梯函数Strictlydecreasing:严格递减Strictlyincreasing:严格递增Sum:和Surface:曲面Surfaceintegral:面积分Surfaceofrevolution:旋转曲面Symmetry:对称R:Radiusofconvergence:收敛半径Rangeofafunction:函数的值域Rateofchange:变化率Rationalfunction:有理函数Rationalizingsubstitution:有理代换法Rationalnumber:有理数Realnumber:实数Rectangularcoordinates:直角坐标Rectangularcoordinatesystem:直角坐标系Relativemaximumandminimum:相对极大值与极小值Revenuefunction:收入函数Revolution,solidof:旋转体Revolution,surfaceof:旋转曲面RiemannSum:黎曼和Riemanniangeometry:黎曼几何Right-handderivative:右导数Right-handlimit:右极限Root:根P、Q:Parabola:拋物线Paraboliccylinder:抛物柱面Paraboloid:抛物面Parallelepiped:平行六面体Parallellines:并行线Parameter:参数Partialderivative:偏导数Partialdifferentialequation:偏微分方程Partialfractions:部分分式Partialintegration:部分积分Partiton:分割Period:周期Periodicfunction:周期函数Perpendicularlines:垂直线Piecewisedefinedfunction:分段定义函数Plane:平面Pointofinflection:反曲点Polaraxis:极轴Polarcoordinate:极坐标Polarequation:极方程式Pole:极点Polynomial:多项式Positiveangle:正角Point-slopeform:点斜式Powerfunction:幂函数Product:积Quadrant:象限QuotientLawoflimit:极限的商定律QuotientRule:商定律M、N、O:Maximumandminimumvalues:极大与极小值MeanValueTheorem:均值定理Multipleintegrals:重积分Multiplier:乘子Naturalexponentialfunction:自然指数函数Naturallogarithmfunction:自然对数函数Naturalnumber:自然数Normalline:法线Normalvector:法向量Number:数Octant:卦限Oddfunction:奇函数One-sidedlimit:单边极限Openinterval:开区间Optimizationproblems:最佳化问题Order:阶Ordinarydifferentialequation:常微分方程Origin:原点Orthogonal:正交的L:Laplacetransform:Leplace变换LawofCosines:余弦定理Leastupperbound:最小上界Left-handderivative:左导数Left-handlimit:左极限Lemniscate:双钮线Length:长度Levelcurve:等高线L'Hospital'srule:洛必达法则Limacon:蚶线Limit:极限Linearapproximation:线性近似Linearequation:线性方程式Linearfunction:线性函数Linearity:线性Linearization:线性化Lineintheplane:平面上之直线Lineinspace:空间之直线Lobachevskigeometry:罗巴切夫斯基几何Localextremum:局部极值Localmaximumandminimum:局部极大值与极小值Logarithm:对数Logarithmicfunction:对数函数I:Implicitdifferentiation:隐求导法Implicitfunction:隐函数Improperintegral:瑕积分Increasing/DecreasingTest:递增或递减试验法Increment:增量IncreasingFunction:增函数Indefiniteintegral:不定积分Independentvariable:自变数Indeterminatefrom:不定型Inequality:不等式Infinitepoint:无穷极限Infiniteseries:无穷级数Inflectionpoint:反曲点Instantaneousvelocity:瞬时速度Integer:整数Integral:积分Integrand:被积分式Integration:积分Integrationbypart:分部积分法Intercepts:截距IntermediatevalueofTheorem:中间值定理Interval:区间Inversefunction:反函数Inversetrigonometricfunction:反三角函数Iteratedintegral:逐次积分H:Highermathematics高等数学/高数E、F、G、H:Ellipse:椭圆Ellipsoid:椭圆体Epicycloid:外摆线Equation:方程式Evenfunction:偶函数ExpectedValued:期望值ExponentialFunction:指数函数Exponents,lawsof:指数率Extremevalue:极值ExtremeValueTheorem:极值定理Factorial:阶乘FirstDerivativeTest:一阶导数试验法Firstoctant:第一卦限Focus:焦点Fractions:分式Function:函数FundamentalTheoremofCalculus:微积分基本定理Geometricseries:几何级数Gradient:梯度Graph:图形GreenFormula:格林公式Half-angleformulas:半角公式Harmonicseries:调和级数Helix:螺旋线HigherDerivative:高阶导数Horizontalasymptote:水平渐近线Horizontalline:水平线Hyperbola:双曲线Hyperboloid:双曲面D:Decreasingfunction:递减函数Decreasingsequence:递减数列Definiteintegral:定积分Degreeofapolynomial:多项式之次数Density:密度Derivative:导数ofacompositefunction:复合函数之导数ofaconstantfunction:常数函数之导数directional:方向导数domainof:导数之定义域ofexponentialfunction:指数函数之导数higher:高阶导数partial:偏导数ofapowerfunction:幂函数之导数ofapowerseries:羃级数之导数ofaproduct:积之导数ofaquotient:商之导数asarateofchange:导数当作变率right-hand:右导数second:二阶导数astheslopeofatangent:导数看成切线之斜率Determinant:行列式Differentiablefunction:可导函数Differential:微分Differentialequation:微分方程partial:偏微分方程Differentiation:求导法implicit:隐求导法partial:偏微分法termbyterm:逐项求导法Directionalderivatives:方向导数Discontinuity:不连续性Diskmethod:圆盘法Distance:距离Divergence:发散Domain:定义域Dotproduct:点积Doubleintegral:二重积分changeofvariablein:二重积分之变数变换inpolarcoordinates:极坐标二重积分C:Calculus:微积分differential:微分学integral:积分学Cartesiancoordinates:笛卡儿坐标一般指直角坐标Cartesiancoordinatessystem:笛卡儿坐标系Cauch'sMeanValueTheorem:柯西均值定理ChainRule:连锁律Changeofvariables:变数变换Circle:圆Circularcylinder:圆柱Closedinterval:封闭区间Coefficient:系数Compositionoffunction:函数之合成Compoundinterest:复利Concavity:凹性Conchoid:蚌线Cone:圆锥Constantfunction:常数函数Constantofintegration:积分常数Continuity:连续性atapoint:在一点处之连续性ofafunction:函数之连续性onaninterval:在区间之连续性fromtheleft:左连续fromtheright:右连续Continuousfunction:连续函数Convergence:收敛intervalof:收敛区间radiusof:收敛半径Convergentsequence:收敛数列series:收敛级数Coordinate:s:坐标Cartesian:笛卡儿坐标cylindrical:柱面坐标polar:极坐标rectangular:直角坐标spherical:球面坐标Coordinateaxes:坐标轴Coordinateplanes:坐标平面Cosinefunction:余弦函数Criticalpoint:临界点Cubicfunction:三次函数Curve:曲线Cylinder:圆柱CylindricalCoordinates:圆柱坐标A、B:Absoluteconvergence:绝对收敛Absoluteextremevalues:绝对极值Absolutemaximumandminimum:绝对极大与极小Absolutevalue:绝对值Absolutevaluefunction:绝对值函数Acceleration:加速度Antiderivative:反导数Approximateintegration:近似积分Approximation:逼近法bydifferentials:用微分逼近linear:线性逼近法bySimpson'sRule:Simpson法则逼近法bytheTrapezoidalRule:梯形法则逼近法Arbitraryconstant:任意常数Arclength:弧长Area:面积underacurve:曲线下方之面积betweencurves:曲线间之面积inpolarcoordinates:极坐标表示之面积ofasectorofacircle:扇形之面积ofasurfaceofarevolution:旋转曲面之面积Asymptote:渐近线horizontal:水平渐近线slant:斜渐近线vertical:垂直渐近线Averagespeed:平均速率Averagevelocity:平均速度Axes,coordinate:坐标轴Axesofellipse:椭圆之轴Binomialseries:二项级数微积分专有名词中英文对照absolutelyconvergent绝对收敛absolutevalue绝对值algebraicfunction代数函数analyticgeometry解析几何antiderivative不定积分approximateintegration近似积分approximation近似法、逼近法arbitraryconstant任意常数arithmeticseries/progression(AP)算数级数asymptotes(verticalandhorizontal)(垂直/水平)渐近线averagerateofchange平均变化率base基数binomialtheorem二项式定理,二项展开式Cartesiancoordinates笛卡儿坐标(一般指直角坐标)Cartesiancoordinatessystem笛卡儿坐标系Cauch'sMeanValueTheorem柯西均值定理chainrule链式求导法则calculus微积分学closedintervalintegral闭区间积分coefficient系数compositefunction复合函数conchoid蚌线continuity(函数的)连续性concavity(函数的)凹凸性conditionallyconvergent有条件收敛continuity连续性criticalpoint临界点cubicfunction三次函数cylindricalcoordinates圆柱坐标decreasingfunction递减函数decreasingsequence递减数列definiteintegral定积分derivative导数determinant行列式differentialcoefficient微分系数differentialequation微分方程directionalderivative方向导数discontinuity不连续性discriminant(二次函数)判别式diskmethod圆盘法divergence散度divergent发散的domain定义域dotproduct点积doubleintegral二重积分ellipse椭圆ellipsoid椭圆体epicycloid外摆线Euler'smethod(BC)欧拉法expectedvalued期望值exponentialfunction指数函数extremevalueheorem极值定理factorial阶乘finiteseries有限级数fundamentaltheoremofcalculus微积分基本定理geometricseries/progression(GP)几何级数gradient梯度Greenformula格林公式half-angleformulas半角公式harmonicseries调和级数helix螺旋线higherderivative高阶导数horizontalasymptote水平渐近线horizontalline水平线hyperbola双曲线hyperboloid双曲面implicitdifferentiation隐函数求导implicitfunction隐函数improperintegral广义积分、瑕积分increment增量increasingfunction增函数indefiniteintegral不定积分independentvariable自变数inequality不等式ndeterminateform不定型infinitepoint无穷极限infiniteseries无穷级数infiniteseries无限级数inflectionpoint(POI)拐点initialcondition初始条件instantaneousrateofchange瞬时变化率integrable可积的integral积分integrand被积分式integration积分integrationbypart分部积分法intercept截距intermediatevalueofTheorem:中间值定理inversefunction反函数irrationalfunction无理函数iteratedintegral逐次积分Laplacetransform拉普拉斯变换lawofcosines余弦定理leastupperbound最小上界left-handderivative左导数left-handlimit左极限L'Hospital'srule洛必达法则limacon蚶线linearapproximation线性近似法linearequation线性方程式linearfunction线性函数linearity线性linearization线性化localmaximum极大值localminimum极小值logarithmicfunction对数函数MacLaurinseries麦克劳林级数maximum最大值meanvaluetheorem(MVT)中值定理minimum最小值methodoflagrangemultipliers拉格朗日乘数法modulus绝对值multipleintegral多重积分multiple倍数multiplier乘子octant卦限openintervalintegral开区间积分optimization优化法,极值法origin原点orthogonal正交parametricequation(BC)参数方程partialderivative偏导数partialdifferentialequation偏微分方程partialfractions部分分式piece-wisefunction分段函数parabola抛物线paraboliccylinder抛物柱面paraboloid:抛物面parallelepiped平行六面体parallellines并行线parameter:参数partialintegration部分积分partiton:分割period:周期periodicfunction周期函数perpendicularlines垂直线piecewisedefinedfunction分段定义函数plane平面pointofinflection反曲点point-slopeform点斜式polaraxis极轴polarcoordinates极坐标polarequation极坐标方程pole极点polynomial多项式powerseries幂级数productrule积的求导法则quadrant象限quadraticfunctions二次函数quotientrule商的求导法则radical根式radiusofconvergence收敛半径range值域(related)rateofchangewithtime(时间)变化率rationalfunction有理函数reciprocal倒数remaindertheorem余数定理Riemannsum黎曼和Riemanniangeometry黎曼几何right-handlimit右极限Rolle'stheorem罗尔(中值)定理root根rotation旋转secantline割线secondderivative二阶导数secondderivativetest二阶导数试验法secondpartialderivative二阶偏导数series级数shellmethod(积分)圆筒法sinefunction正弦函数singularity奇点slant母线slantasymptote斜渐近线slope斜率slope-interceptequationofaline直线的斜截式smoothcurve平滑曲线smoothsurface平滑曲面solidofrevolution旋转体symmetry对称性substitution代入法、变量代换tangentfunction正切函数tangentline切线tangentplane切(平)面tangentvector切矢量taylor'sseries泰勒级数three-dimensionalanalyticgeometry空间解析几何totaldifferentiation全微分trapezoidrule梯形(积分)法则