微积分双语常用词汇

MATHEMATICALTERMS(Part1)calculus微积分definition定义theorem定理lemma引理corollary推论prove证明proof证明show证明solution解formula公式ifandonlyif(iff)当且仅当xXforallxXxXthereexistsanxXsuchthat使得given已知set集合finiteset有限集infiniteset无限集interval区间openinterval开区间closedinterval闭区间neighborhood邻域number数naturalnumber自然数integer整数oddnumber奇数evennumber偶数realnumber实数rationalnumber有理数irrationalnumber无理数positivenumber正数negativenumber负数mapping映射function函数monotonefunction单调函数increasingfunction增函数decreasingfunction减函数boundedfunction有界函数oddfunction奇函数evenfunction偶函数periodicfunction周期函数compositefunction复合函数inversefunction反函数domain定义域range值域variable变量independentvariable自变量dependentvariable因变量sequence数列convergentsequence收敛数列divergentsequence发散数列boundedsequence有界数列decreasingsequence递减数列increasingsequence递增数列limit极限one-sidedlimit单侧极限left-handlimit左极限right-handlimit右极限TheSqueezeTheorem夹挤定理infinity无穷大infinitesimal无穷小equivalentinfinitesimal等价无穷小infinitesimalofhigherorder高阶无穷小orderofinfinitesimal无穷小的阶infinitesimalsofthesameorder同阶无穷小increment增量continuousfunction持续函数continuity持续性f(x)iscontinuousatx在x持续f(x)isdiscontinuousatx在x间断discontinuity间断点discontinuityofthefirst(second)kind第一（二）类间断点removablediscontinuity可去间断点jumpdiscontinuity跳跃间断点infinitediscontinuity无穷间断点intermediatevalue介值TheIntermediateValueTheorem介值定理zeropoint零点TheZeroPointTheorem零点定理root根equation方程uniformcontinuity一致持续derivative导数rateofchange变化率velocity速度instantaneousvelocity瞬时速度tangent(line)切线normal(line)法线slope斜率left-handderivative左导数right-handderivative右导数f(x)isdifferentiableatxf(x)在x处可导(可微)differentiation求导TheChainRule链式法则differentiationformulas求导公式implicitfunction隐函数explicitfunction显函数implicitdifferentiation隐函数求导logarithm对数Logarithmicdifferentiation对数求导法parameter参数parametricequation参数方程parametriccurve参数曲线hyperbolicfunction双曲函数hyperbolicsine双曲正弦hyperboliccosine双曲余弦hyperbolictangent双曲正切hyperboliccotangent双曲余切MATHEMATICALTERMS(Part2)differential微分differentialquotient微商approximatevalue近似值error误差relativeerror相对误差absoluteerror绝对误差invarianceofdifferentialform微分形式不变性higherderivative高阶导数firstderivative一阶导数secondderivative二阶导数thirdderivative三阶导数nthderivativen阶导数twicedifferentiable二阶可导acceleration加速度meanvalue中值TheMeanValueTheorem中值定理Rolle’sTheorem罗尔定理Lagrange’sMeanValueTheorem拉格朗日中值定理Cauchy’sMeanValueTheorem柯西中值定理equality等式inequality不等式indeterminateform不定型(未定式)indeterminateformoftype00()00()型未定式L’Hospital’sRule洛必达法则Taylor’sformula泰勒公式polynomial多项式nth-degreepolynomialn次多项式remaind余项Lagrange’sformofremainder拉格朗日型余项Peano’sformofremainder皮亚诺型余项Maclaurinformula麦克劳林公式Taylorpolynomial泰勒多项式Mauclaurinpolynomial麦克劳林多项式polynomialapproximation多项式逼近accuracy精确度margin边际marginalcost边际成本marginalrevenue边际收益elasticity弹性density密度mass质量extremevalue极值localmaximumvalue极大值localminimumvalue极小值(absolute)maximum最大值(absolute)minimum最小值stationarypoint驻点（稳定点）criticalpoint临界点TheFirst(Second)DerivativeTest（极值的）一（二）阶鉴别法convex凸的convexcurve凸曲线concave凹的concavecurve凹曲线convexfunction凸函数pointofinflection拐点asymptote渐近线horizontalasymptote水平渐近线verticalasymptote垂直渐近线slantasymptote斜渐近线curvesketching作图sketchacurve作图curvature曲率Thebisectionmethod二分法Thesecantmethod弦位法Newton’smethod牛顿（切线）法Thetangentmethod切线法differentialcalculus微分学integral积分integralcalculus积分学definiteintegral定积分indefiniteintegral不定积分partition分割Riemannsum黎曼和integralsign积分符号integrand被积函数upper(lower)limitofintegration积分上（下）限integration积分（求积）integrable可积的f(x)isintegrableon[a,b]integrablefunction可积函数integrability可积性sufficientcondition充足条件necessarycondition必要条件piecewisecontinuous分段持续property性质Themeanvaluetheoremofintegral积分中值定理Thefundamentaltheoremofcalculus微积分基本定理Newton-Leibnizformulaprimitivefunction(anti-derivative)原函数（反导数）Thesubstitutionruleforintegration换元积分法Theinverseofthechainrule反链式法（凑微分法）integrationbyparts分部积分法rationalfunction有理函数fraction分式irreduciblefraction最简分式partialfraction部分分式partialfractiondecomposition部分分式分解MATHEMATICALTERMS(Part3)vector矢量freevector自由矢量zerovector零矢量magnitudeofavector矢量的模unitvector单位矢量scalarproduct数量积dotproduct点积vectorproduct矢量积crossproduct叉积aisperpendicular(orthogonal)toba与b垂直coordinate坐标coordinatesystem坐标系coordinateaxis坐标轴x-axisx轴coordinateplane坐标面directionangle方向角directioncosine方向余弦rectangularcoordinatesystem直角坐标系octant卦限thefirstoctant第一卦限variable变量functionoftwo(three)variables二（三）元函数functionofseveralvariables多元函数independentvariable自变量dependentvariable因变量domain定义域range值域setofpoints点集neighborhood邻域interiorpoint内点boundarypoint边界点bound边界openset开集closedset闭集connectedset连通集region区域openregion开区域closedregion闭区域boundedregion有界区域unboundedregion无界区域clusterpoint聚点doublelimit二重极限iteratedlimit累次极限continuity持续性increment增量totalincrement全增量partialincrement偏增量partialderivative偏导数partialderivativeoff(x,y)withrespecttox(y)f(x,y)有关x（y）的偏导数higherpartialderivative高阶偏导数mixedpartialderivative混合偏导数Laplaceequation拉普拉斯方程totaldifferential全微分differentiable可微chainrule链式法则implicitfunction隐函数implicitdifferentiation隐函数微分法Jacobiandeterminant雅可比行列式curve曲线spacecurve空间曲线tangentvector切矢tangentline切线normalplane法平面surface曲面normalvector法矢normalline法线tangentplane切平面sphere球面cylinder柱面cone锥面directionalderivative方向导数gradient梯度gradientvector梯度矢量fdelflevelcurve等值线levelsurface等值面localextremum极值localmaximum极大值localminimum极小值extremevalue最值absolutemaximum(minimum)最大（最小）值stationarypoint(criticalpoint)驻点（临界点）conditionalextremum条件极值Lagrangemultiplier拉格朗日乘数methodofLagrangemultiplier拉格朗日乘数法objectivefunction目的函数constraint约束条件methodofleastsquare最小二乘法field场scalarfield数量场vectorfield矢量场gradientfield梯度场potentialfield势场potentialfunction势函数conservativefield保守场gravitationalfield引力场forcefield力场velocityfield速度场MATHEMATICALTERMS(Part4)multipleintegral重积分doubleintegral二重积分iteratedintegral累次积分region区域regionofintegration积分区域typeX(Y)regionX（Y）型区域orderofintegration积分秩序reversetheorderofintegration交换积分秩序polarcoordinates极坐标doubleintegralsinpolarcoordinates极坐标下的二重积分volume体积lamina平面薄片mass质量density密度momentaboutx-axis有关x轴的（静）力矩centerofmass重心momentofinertia转动惯量surface曲面areaofasurface曲面的面积tripleintegral三重积分rectangle矩形rectangularcoordinates直角坐标系cylinder柱面cylindricalcoordinates柱面坐标系sphere球面sphericalcoordinates球面坐标系changeofvariablesinmultipleintegrals重积分的变量替代Jacobiandeterminant雅可比行列式lineintegral曲线积分lineintegralwithrespecttoarclength对弧长的曲线积分（第一型）lineintegralwithrespecttox(y)对坐标x（y）曲线积分（第二型）lineintegralofavectorfield向量场的曲线积分smoothcurve光滑曲线piecewisesmoothcurve逐