微積分雙語常用詞匯

1、MATHEMATICALTERMS(Part1)calculus微積分definition定義theorem定理lemma引理corollary推論prove證實proof證實show證實solution解formula公式ifandonlyif(iff)當(dāng)且僅當(dāng)-xXforallxXxXthereexistsanxXsuchthat使得givenset集合finiteset有限集infiniteset無限集interval區(qū)間openinterval開區(qū)間closedinterval閉區(qū)間neighborhood令B域number數(shù)naturalnumber自然數(shù)integer整數(shù)oddnu

2、mber奇數(shù)evennumber偶數(shù)realnumber實數(shù)rationalnumber有理數(shù)irrationalnumber無理數(shù)positivenumber正數(shù)negativenumber負(fù)數(shù)mapping映射function函數(shù)monotonefunction單調(diào)函數(shù)increasingfunction增函數(shù)decreasingfunction減函數(shù)boundedfunction有界函數(shù)oddfunction奇函數(shù)evenfunction偶函數(shù)periodicfunction周期函數(shù)compositefunction復(fù)合函數(shù)inversefunction反函數(shù)domain定義域range

3、值域variable變量independentvariable自變量dependentvariable因變量sequence數(shù)歹Uconvergentsequence收斂數(shù)歹Udivergentsequence發(fā)散數(shù)列boundedsequence有界數(shù)歹Udecreasingsequence遞減數(shù)歹Uincreasingsequence遞增數(shù)歹Ulimit極限one-sidedlimit單側(cè)極限left-handlimit左極限r(nóng)ight-handlimit右極限TheSqueezeTheorem夾擠定理infinity無窮大infinitesimal無窮小equivalentinfinit

4、esimal等價無窮小infinitesimalofhigherorder高階無窮小orderofinfinitesimal無窮/卜的階infinitesimalsofthesameorder同階無窮小increment增量continuousfunction連續(xù)函數(shù)continuity連續(xù)性f(x)iscontinuousatx在x連續(xù)f(x)isdiscontinuousatx在x間斷discontinuity間斷點discontinuityofthefirst(second)kind第一(二)類間斷點removablediscontinuity可去間斷點jumpdiscontinuity

5、跳躍間斷點infinitediscontinuity無窮間斷點intermediatevalue介值TheIntermediateValueTheorem介值定理zeropoint零點TheZeroPointTheorem零點定理root根equation方程uniformcontinuity一致連續(xù)derivative導(dǎo)數(shù)rateofchange變化率velocity速度instantaneousvelocity瞬時速度tangent(line)切線normal(line)法線slope斜率left-handderivative左導(dǎo)數(shù)right-handderivative右導(dǎo)數(shù)f(x)is

6、differentiableatxf(x)在x處可導(dǎo)(可微)differentiation求導(dǎo)TheChainRule鏈?zhǔn)椒敲磀ifferentiationformulas求導(dǎo)公式implicitfunction隱函數(shù)explicitfunction顯函數(shù)隱函數(shù)求導(dǎo)對數(shù)求導(dǎo)法implicitdifferentiationlogarithm對數(shù)Logarithmicdifferentiationparameter參數(shù)parametricequation參數(shù)方程parametriccurve參數(shù)曲線hyperbolicfunction雙曲函數(shù)hyperbolicsine雙曲正弦hyperboli

7、ccosine雙曲余弦hyperbolictangent雙曲正切hyperboliccotangent雙曲余切MATHEMATICALTERMS(Part2)differential微分differentialquotient微商approximatevalue近似值error誤差relativeerror相對誤差absoluteerror絕對誤差invarianceofdifferentialform微分形式不變性higherderivative高階導(dǎo)數(shù)firstderivative一階導(dǎo)數(shù)secondderivative二階導(dǎo)數(shù)thirdderivative三階導(dǎo)數(shù)nthderivativ

8、en階導(dǎo)數(shù)twicedifferentiable二階可導(dǎo)acceleration力口速度meanvalue中值TheMeanValueTheorem中值定理Rolle'sTheorem羅爾定理Lagrange'sMeanValueTheorem拉格朗日中值定理Cauchy'sMeanValueTheorem柯西甲值定理equality等式inequality不等式indeterminateform不定型未定式indeterminateformoftype00二00電型未定式Hospital'sRule洛必達(dá)法那么Taylor'sformula泰勒公式po

9、lynomial多項式nth-degreepolynomialn次多項式remaind余項Lagrange'sformofremainder拉格朗日型余項Peano'sformofremainder皮亞諾型余項Maclaurinformula麥克勞林公式Taylorpolynomial泰勒多項式Mauclaurinpolynomial麥克勞林多項式polynomialapproximation多項式逼近accuracy精確度margin邊際marginalcost邊際本錢marginalrevenue邊際收益elasticity彈性density密度mass質(zhì)量extremev

10、alue極值localmaximumvalue極大值localminimumvalue極小值absolutemaximum最大值absoluteminimum最小值stationarypoint駐點穩(wěn)定點criticalpoint臨界點TheFirstSecondDerivativeTest極值的一二階判別法convex凸的convexcurve凸曲線concave凹的concavecurve凹曲線convexfunction凸函數(shù)pointofinflection拐點asymptote漸近線horizontalasymptote水平漸近線verticalasymptote垂直漸近線slant

11、asymptote斜漸近線curvesketching作圖sketchacurve作圖curvature曲率Thebisectionmethod二分法Thesecantmethod弦位法Newton'smethod牛頓切線法Thetangentmethod切線法differentialcalculus微分學(xué)integral積分integralcalculus積分學(xué)definiteintegral定積分indefiniteintegral不定積分partition分割Riemannsum黎曼和integralsign積分符號integrand被積函數(shù)upperlowerlimitofin

12、tegration積分上下限integration積分求積integrable可積的fxisintegrableona,bintegrablefunction可積函數(shù)integrability可積性sufficientcondition充分條件necessarycondition必要條件piecewisecontinuous分段連續(xù)property性質(zhì)積分中值定理微積分根本定理原函數(shù)反導(dǎo)數(shù)換元積分法反鏈?zhǔn)椒愇⒎址═hemeanvaluetheoremofintegralThefundamentaltheoremofcalculusNewton-Leibnizformulaprimitivef

13、unction(anti-derivative)ThesubstitutionruleforintegrationTheinverseofthechainruleintegrationbyparts分部積分法rationalfunction有理函數(shù)fraction分式irreduciblefraction最簡分式partialfraction局部分式partialfractiondecomposition局部分式分解MATHEMATICALTERMS(Part3)vector矢量freevector自由矢量zerovector零矢量magnitudeofavector矢量的模unitvecto

14、r單位矢量scalarproduct數(shù)量積dotproduct點積vectorproduct矢量積crossproduct叉積aisperpendicular(orthogonal)toba與b垂直coordinate坐標(biāo)coordinatesystem坐標(biāo)系coordinateaxis坐標(biāo)軸x-axisx軸coordinateplane坐標(biāo)面directionangle方向角directioncosine方向余弦直角坐標(biāo)系rectangularcoordinatesystemoctant圭卜限thefirstoctant第圭卜限variable變量functionoftwo(three)va

15、riables二(三)元函數(shù)functionofseveralvariables多元函數(shù)independentvariable自變量dependentvariable因變量domain定義域range值域setofpointsneighborhood令B域interiorpoint內(nèi)點boundarypoint邊界點bound邊界openset開集closedset閉集connectedset連通集region區(qū)域openregion開區(qū)域closedregion閉區(qū)域boundedregion有界區(qū)域unboundedregion無界區(qū)域clusterpoint聚點doublelimit二重

16、極限iteratedlimit累次極限continuity連續(xù)性increment增量totalincrement全增量partialincrement偏增量partialderivative偏導(dǎo)數(shù)partialderivativeoff(x,y)withrespecttox(y)f(x,y)關(guān)于x(y)的偏導(dǎo)數(shù)higherpartialderivative高階偏導(dǎo)數(shù)mixedpartialderivative混合偏導(dǎo)數(shù)Laplaceequation拉普拉斯方程totaldifferential全微分differentiable可微chainrule鏈?zhǔn)椒敲磇mplicitfunction隱

17、函數(shù)implicitdifferentiation隱函數(shù)微分法Jacobiandeterminant雅可比行歹U式curve曲線spacecurve空間曲線tangentvector切矢tangentline切線normalplane法平面surface曲面normalvector法矢normalline法線tangentplane切平面sphere球面cylinder柱面cone錐面directionalderivative方向?qū)?shù)gradient梯度gradientvector梯度矢量'fdelflevelcurve等值線levelsurface等值面localextremum極值

18、localmaximum極大值localminimum極小值extremevalue最值absolutemaximum(minimum)最大(最小)值stationarypoint(criticalpoint)駐點(臨界點)conditionalextremum條件極值Lagrangemultiplier拉格朗日乘數(shù)methodofLagrangemultiplier拉格朗日乘數(shù)法objectivefunction目標(biāo)函數(shù)constraint約束條件methodofleastsquare最小二乘法field場scalarfield數(shù)量場vectorfield矢量場gradientfield梯度

19、場potentialfield勢場potentialfunction勢函數(shù)conservativefield保守場gravitationalfield弓I力場forcefield力場velocityfield速度場MATHEMATICALTERMS(Part4)multipleintegral重積分doubleintegral二重積分iteratedintegral累次積分region區(qū)域regionofintegration積分區(qū)域typeX(Y)regionX(丫)型區(qū)域orderofintegration積分秩序reversetheorderofintegration交換積分秩序pola

20、rcoordinates極坐標(biāo)doubleintegralsinpolarcoordinates極坐標(biāo)下的二重積分volume體積lamina平面薄片mass質(zhì)量density密度momentaboutx-axis關(guān)于x軸的靜力矩centerofmass重心momentofinertia轉(zhuǎn)動慣量surface曲面areaofasurface曲面的面積tripleintegral三重積分rectangle矩形rectangularcoordinates直角坐標(biāo)系cylinder柱面cylindricalcoordinates柱面坐標(biāo)系sphere球面sphericalcoordinates球面坐標(biāo)系重積分的變對弧長的曲對坐標(biāo)xy曲changeofvariablesinmultipleintegrals量替換Jacobiandeterminant雅可比行歹U式lineintegral曲線積分lineintegralwithrespecttoarclength線積分第一型lineintegralwithrespecttoxy線積分第二型lineintegralofavectorfield向量場的曲線積分smoothcurve光滑曲線piecewisesmoothc