英漢微積分詞匯

第一部分英漢微積分詞匯Part1English-ChineseCalculusVocabulary第一章函數(shù)與極限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補集complementset直積directproduct笛卡兒積Cartesianproduct開區(qū)間openinterval閉區(qū)間closedinterval半開區(qū)間halfopeninterval有限區(qū)間finiteinterval區(qū)間的長度lengthofaninterval無限區(qū)間infiniteinterval領域neighborhood領域的中心centreofaneighborhood領域的半徑radiusofaneighborhood左領域leftneighborhood右領域rightneighborhood映射mappingX到Y的映射mappingofXontoY滿射surjection單射injection一一映射one-to-onemapping雙射bijection算子operator變化transformation函數(shù)function逆映射inversemapping復合映射compositemapping自變量independentvariable因變量dependentvariable定義域domain函數(shù)值valueoffunction函數(shù)關系functionrelation值域range自然定義域naturaldomain單值函數(shù)singlevaluedfunction多值函數(shù)multiplevaluedfunction單值分支one-valuedbranch函數(shù)圖形graphofafunction絕對值函數(shù)absolutevalue符號函數(shù)sighfunction整數(shù)部分integralpart階梯曲線stepcurve當且僅當ifandonlyif(iff)分段函數(shù)piecewisefunction上界upperbound下界lowerbound有界boundedness無界unbounded函數(shù)的單調性monotonicityofafunction單調增加的increasing單調減少的decreasing單調函數(shù)monotonefunction函數(shù)的奇偶性parity(odevity)ofafunction對稱symmetry偶函數(shù)evenfunction奇函數(shù)oddfunction函數(shù)的周期性periodicityofafunction周期period反函數(shù)inversefunction直接函數(shù)directfunction復合函數(shù)compositefunction中間變量intermediatevariable函數(shù)的運算operationoffunction基本初等函數(shù)basicelementaryfunction初等函數(shù)elementaryfunction冪函數(shù)powerfunction指數(shù)函數(shù)exponentialfunction對數(shù)函數(shù)logarithmicfunction三角函數(shù)trigonometricfunction反三角函數(shù)inversetrigonometricfunction常數(shù)函數(shù)constantfunction雙曲函數(shù)hyperbolicfunction雙曲正弦hyperbolicsine雙曲余弦hyperboliccosine雙曲正切hyperbolictangent反雙曲正弦inversehyperbolicsine反雙曲余弦inversehyperboliccosine反雙曲正切inversehyperbolictangent極限limit數(shù)列sequenceofnumber收斂convergence收斂于aconvergetoa發(fā)散divergent極限的唯一性uniquenessoflimits收斂數(shù)列的有界性boundednessofaconvergentsequence子列subsequence函數(shù)的極限limitsoffunctions函數(shù)當x趨于x0時的極限limitoffunctionsasxapproachesx0左極限leftlimit右極限rightlimit單側極限one-sidedlimits水平漸近線horizontalasymptote無窮小infinitesimal無窮大infinity鉛直漸近線verticalasymptote夾逼準則squeezerule單調數(shù)列monotonicsequence高階無窮小infinitesimalofhigherorder低階無窮小infinitesimaloflowerorder同階無窮小infinitesimalofthesameorder等階無窮小equivalentinfinitesimal函數(shù)的連續(xù)性continuityofafunction增量increment函數(shù)在x0連續(xù)thefunctioniscontinuousatx0左連續(xù)leftcontinuous右連續(xù)rightcontinuous區(qū)間上的連續(xù)函數(shù)continuousfunction函數(shù)在該區(qū)間上連續(xù)functioniscontinuousonaninterval不連續(xù)點discontinuitypoint第一類間斷點discontinuitypointofthefirstkind第二類間斷點discontinuitypointofthesecondkind初等函數(shù)的連續(xù)性continuityoftheelementaryfunctions定義區(qū)間definedinterval最大值globalmaximumvalue(absolutemaximum)最小值globalminimumvalue(absoluteminimum)零點定理thezeropointtheorem介值定理intermediatevaluetheorem第二章導數(shù)與微分Chapter2DerivativeandDifferential速度velocity勻速運動uniformmotion平均速度averagevelocity瞬時速度instantaneousvelocity圓的切線tangentlineofacircle切線tangentline切線的斜率slopeofthetangentline位置函數(shù)positionfunction導數(shù)derivative可導derivable函數(shù)的變化率問題problemofthechangerateofafunction導函數(shù)derivedfunction左導數(shù)left-handderivative右導數(shù)right-handderivative單側導數(shù)one-sidedderivatives在閉區(qū)間【a,b】上可導isderivableontheclosedinterval[a,b]切線方程tangentequation角速度angularvelocity成本函數(shù)costfunction邊際成本marginalcost鏈式法則chainrule隱函數(shù)implicitfunction顯函數(shù)explicitfunction二階函數(shù)secondderivative三階導數(shù)thirdderivative高階導數(shù)nthderivative萊布尼茨公式Leibnizformula對數(shù)求導法log-derivative參數(shù)方程parametricequation相關變化率correlativechangerata微分differential可微的differentiable函數(shù)的微分differentialoffunction自變量的微分differentialofindependentvariable微商differentialquotient間接測量誤差indirectmeasurementerror絕對誤差absoluteerror相對誤差relativeerror第三章微分中值定理與導數(shù)的應用Chapter3MeanValueTheoremofDifferentialsandtheApplicationofDerivatives羅馬定理Rolle’stheorem費馬引理Fermat’slemma拉格朗日中值定理Lagrange’smeanvaluetheorem駐點stationarypoint穩(wěn)定點stablepoint臨界點criticalpoint輔助函數(shù)auxiliaryfunction拉格朗日中值公式Lagrange’smeanvalueformula柯西中值定理Cauchy’smeanvaluetheorem洛必達法則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余項remainderterm拉格朗日余項Lagrangeremainderterm麥克勞林公式Maclaurin’sformula佩亞諾公式Peanoremainderterm凹凸性concavity凹向上的concaveupward,cancaveup凹向下的，向上凸的concavedownward’concavedown拐點inflectionpoint函數(shù)的極值extremumoffunction極大值local(relative)maximum最大值global(absolute)mximum極小值local(relative)minimum最小值global(absolute)minimum目標函數(shù)objectivefunction曲率curvature弧微分arcdifferential平均曲率averagecurvature曲率園circleofcurvature曲率中心centerofcurvature曲率半徑radiusofcurvature漸屈線evolute漸伸線involute根的隔離isolationofroot隔離區(qū)間isolationinterval切線法tangentlinemethod第四章不定積分Chapter4IndefiniteIntegrals原函數(shù)primitivefunction(antiderivative)積分號signofintegration被積函數(shù)integrand積分變量integralvariable積分曲線integralcurve積分表tableofintegrals換元積分法integrationbysubstitution分部積分法integrationbyparts分部積分公式formulaofintegrationbyparts有理函數(shù)rationalfunction真分式properfraction假分式improperfraction第五章定積分Chapter5DefiniteIntegrals曲邊梯形trapezoidwith曲邊curveedge窄矩形narrowrectangle曲邊梯形的面積areaoftrapezoidwithcurvededge積分下限lowerlimitofintegral積分上限upperlimitofintegral積分區(qū)間integralinterval分割partition積分和integralsum可積integrable矩形法rectanglemethod積分中值定理meanvaluetheoremofintegrals函數(shù)在區(qū)間上的平均值averagevalueofafunctiononanintegvals牛頓－萊布尼茨公式Newton-Leibnizformula微積分基本公式fundamentalformulaofcalculus換元公式formulaforintegrationbysubstitution遞推公式recurrenceformula反常積分improperintegral反常積分發(fā)散theimproperintegralisdivergent反常積分收斂theimproperintegralisconvergent無窮限的反常積分improperintegralonaninfiniteinterval無界函數(shù)的反常積分improperintegralofunboundedfunctions絕對收斂absolutelyconvergent第六章定積分的應用Chapter6ApplicationsoftheDefiniteIntegrals元素法theelementmethod面積元素elementofarea平面圖形的面積areaofaluanefigure直角坐標又稱“笛卡兒坐標(Cartesiancoordinates)”極坐標polarcoordinates拋物線parabola橢圓ellipse旋轉體的面積volumeofasolidofrotation旋轉橢球體ellipsoidofrevolution,ellipsoidofrotation曲線的弧長arclengthofacurve可求長的rectifiable光滑smooth功work水壓力waterpressure引力gravitation變力variableforce第七章空間解析幾何與向量代數(shù)Chapter7SpaceAnalyticGeometryandVectorAlgebra向量vector自由向量freevector單位向量unitvector零向量zerovector相等equal平行parallel向量的線性運算linearpoerationofvector三角法則trianglerule平行四邊形法則parallelogramrule交換律commutativelaw結合律associativelaw負向量negativevector差difference分配律distributivelaw空間直角坐標系spacerectangularcoordinates坐標面coordinateplane卦限octant向量的模modulusofvector向量a與b的夾角anglebetweenvectoraandb方向余弦directioncosine方向角directionangle向量在軸上的投影projectionofavectorontoanaxis數(shù)量積，外積，叉積scalarproduct,dotproduct,innerproduct曲面方程equationforasurface球面sphere旋轉曲面surfaceofrevolution母線generatingline軸axis圓錐面cone頂點vertex旋轉單葉雙曲面revolutionhyperboloidsofonesheet旋轉雙葉雙曲面revolutionhyperboloidsoftwosheets柱面cylindricalsurface,cylinder圓柱面cylindricalsurface準線directrix拋物柱面paraboliccylinder二次曲面quadricsurface橢圓錐面dllipticcone橢球面ellipsoid單葉雙曲面hyperboloidofonesheet雙葉雙曲面hyperboloidoftwosheets旋轉橢球面ellipsoidofrevolution橢圓拋物面ellipticparaboloid旋轉拋物面paraboloidofrevolution雙曲拋物面hyperbolicparaboloid馬鞍面saddlesurface橢圓柱面ellipticcylinder雙曲柱面hyperboliccylinder拋物柱面paraboliccylinder空間曲線spacecurve空間曲線的一般方程generalformequationsofaspacecurve空間曲線的參數(shù)方程parametricequationsofaspacecurve螺轉線spiral螺矩pitch投影柱面projectingcylinder投影projection平面的點法式方程pointnormformeqyationofaplane法向量normalvector平面的一般方程generalformequationofaplane兩平面的夾角anglebetweentwoplanes點到平面的距離distancefromapointtoaplane空間直線的一般方程generalequationofalineinspace方向向量directionvector直線的點向式方程pointdirectionformequationsofaline方向數(shù)directionnumber直線的參數(shù)方程parametricequationsofaline兩直線的夾角anglebetweentwolines垂直perpendicular直線與平面的夾角anglebetweenalineandaplanes平面束pencilofplanes平面束的方程equationofapencilofplanes行列式determinant系數(shù)行列式coefficientdeterminant第八章多元函數(shù)微分法及其應用Chapter8DifferentiationofFunctionsofSeveralVariablesandItsApplication一元函數(shù)functionofonevariable多元函數(shù)functionofseveralvariables內點interiorpoint外點exteriorpoint邊界點frontierpoint,boundarypoint聚點pointofaccumulation開集openset閉集closedset連通集connectedset開區(qū)域openregion閉區(qū)域closedregion有界集boundedset無界集unboundedsetn維空間n-dimentionalspace二重極限doublelimit多元函數(shù)的連續(xù)性continuityoffunctionofseveal連續(xù)函數(shù)continuousfunction不連續(xù)點discontinuitypoint一致連續(xù)uniformlycontinuous偏導數(shù)partialderivative對自變量x的偏導數(shù)partialderivativewithrespecttoindependentvariablex高階偏導數(shù)partialderivativeofhigherorder二階偏導數(shù)secondorderpartialderivative混合偏導數(shù)hybridpartialderivative全微分totaldifferential偏增量oartialincrement偏微分partialdifferential全增量totalincrement可微分differentiable必要條件necessarycondition充分條件sufficientcondition疊加原理superpostitionprinciple全導數(shù)totalderivative中間變量intermediatevariable隱函數(shù)存在定理theoremoftheexistenceofimplicitfunction曲線的切向量tangentvectorofacurve法平面normalplane向量方程vectorequation向量值函數(shù)vector-valuedfunction切平面tangentplane法線normalline方向導數(shù)directionalderivative梯度gradient數(shù)量場scalarfield梯度場gradientfield向量場vectorfield勢場potentialfield引力場gravitationalfield引力勢gravitationalpotential曲面在一點的切平面tangentplanetoasurfaceatapoint曲線在一點的法線normallinetoasurfaceatapoint無條件極值unconditionalextremevalues條件極值conditionalextremevalues拉格朗日乘數(shù)法Lagrangemultipliermethod拉格朗日乘子Lagrangemultiplier經(jīng)驗公式empiricalformula最小二乘法methodofleastsquares均方誤差meansquareerror重積分Chapter9MultipleIntegrals二重積分doubleintegral可加性additivity累次積分iteratedintegral體積元素volumeelement三重積分tripleintegral直角坐標系中的體積元素volumeelementinrectangularcoordinatesystem柱面坐標cylindricalcoordinates柱面坐標系中的體積元素volumeelementincylindricalcoordinatesystem球面坐標sphericalcoordinates球面坐標系中的體積元素volumeelementinsphericalcoordinatesystem反常二重積分improperdoubleintegral曲面的面積areaofasurface質心centreofmass靜矩staticmoment密度density形心centroid轉動慣量momentofinertia參變量parametricvariable曲線積分與曲面積分Chapter10Line(Curve)IntegralsandSurfaceIntegrals對弧長的曲線積分lineintegralswithrespecttoarchength第一類曲線積分lineintegralsofthefirsttype對坐標的曲線積分lineintegralswithrespecttox,y,andz第二類曲線積分lineintegralsofthesecondtype有向曲線弧directedarc單連通區(qū)域simpleconnectedregion復連通區(qū)域complexconnectedregion格林公式Greenformula第一類曲面積分surfaceintegralsofthefirsttype對面的曲面積分surfaceintegralswithrespecttoarea有向曲面directedsurface對坐標的曲面積分surfaceintegralswithrespecttocoordinateelements第二類曲面積分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環(huán)流量circulation旋度rotation,curl無窮級數(shù)Chapter11InfiniteSeries一般項generalterm部分和partialsum余項remainderterm等比級數(shù)geometricseries幾何級數(shù)geometricseries公比commonratio調和級數(shù)harmonicseries柯西收斂準則Cauchyconvergencecriteria,Cauchycriteriaforconvergence正項級數(shù)seriesofpositiveterms達朗貝爾判別法D’Alemberttest柯西判別法Cauchytest交錯級數(shù)alternatingseries絕對收斂absolutelyconvergent條件收斂conditionallyconvergent柯西乘積Cauchyproduct函數(shù)項級數(shù)seriesoffunctions發(fā)散點pointofdivergence收斂點pointofconvergence收斂域convergencedomain和函數(shù)sumfunction冪級數(shù)powerseries冪級數(shù)的系數(shù)coeffcientsofpowerseries阿貝爾定理AbelTheorem收斂半徑radiusofconvergence收斂區(qū)間intervalofconvergence泰勒級數(shù)Taylorseries麥克勞林級數(shù)Maclaurinseries二項展開式binomialexpansion近似計算approximatecalculation舍入誤差round-offerror,roundingerror歐拉公式Euler’sformula魏爾斯特拉絲判別法Weierstrasstest三角級數(shù)trigonometricseries振幅amplitude角頻率angularfrequency初相initialphase矩形波squarewave諧波分析harmonicanalysis直流分量directcomponent基波fundamentalwave二次諧波secondharmonic三角函數(shù)系trigonometricfunctionsystem傅立葉系數(shù)Fouriercoefficient傅立葉級數(shù)Forrierseries周期延拓periodicprolongation正弦級數(shù)sineseries余弦級數(shù)cosineseries奇延拓oddprolongation偶延拓evenprolongation傅立葉級數(shù)的復數(shù)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微分方程的階orderofadifferentialequation微分方程的解solutionofadifferentialequation微分方程的通解generalsolutionofadifferentialequation初始條件initialcondition微分方程的特解particularsolutionofadifferentialequation初值問題initialvalueproblem微分方程的積分曲線integralcurveofadifferentialequation可分離變量的微分方程variableseparabledifferentialequation隱式解implicitsolution隱式通解