数学英汉词典

1、数学英汉词典-微积分MATHEMATICAL TERMS (Part 1)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i

2、nteger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d

3、omain定义域range值域variable变量independentvariable自变量dependentvariable因变量sequence数歹！Jconvergentsequence攵敛数歹！Jdivergentsequence发散数歹！Jboundedsequence有界数歹！Jdecreasingsequence减数歹Uincreasingsequence递增数歹！Jlimit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

4、小equivalentinfinitesimal等价无穷小infinitesimalofhigherorder高阶无穷小orderofinfinitesimal无穷小的8阶infinitesimalsofthesameorder同阶无穷小increment增量continuousfunction连续函数continuity连续性f(x)iscontinuousatx在x连续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j

5、umpdiscontinuity跳跃间断点infinitediscontinuity无穷间断点intermediatevalue介值TheIntermediateValueTheorem介值定理zeropoint零点点TheZeroPointTheorem零点定理root根equation方程uniformcontinuity一致连续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-handde

6、rivative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hyperbolics

7、ine双曲正弦hyperboliccosine双曲余弦hyperbolictangent双曲正切hyperboliccotangent双曲余切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twi

8、cedifferentiable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)indeterminateformoftype0(一)0(一)型未定式L'Hospital'sR#le、达法则Taylor'sformula泰勒公式pol

9、ynomial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extremeva

10、lue极值localmaximumvalue极大值localminimumvalue极小值(absolute)maximum最大值(absolute)minimum最小值stationarypoint驻点用急定八、criticalpoint临界点TheFirst(Second)DerivativeTest极值的一二阶判别法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

11、近线slantasymptote斜渐近线curvesketching作图sketchacurve作图curvature曲率Thebisectionmethod二分法Thesecantmethod弦位法Newtonsmethod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integration积分求积integrable可积的f(x)isintegrableona,bintegrablefunction可积函数

12、integrability可积性sufficientcondition充分条件necessarycondition必要条件piecewisecontinuous分段连续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in

13、tegrationbyparts分部积分法分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vector矢量freevector自由矢量zerovector零矢量magnitudeofavector矢量的模unitvector单位矢量scalarproduct

14、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functio

15、nofseveralvariables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聚点点doublelimit二重极限iteratedlimit累次极限

16、continuity连续性increment增量totalincrement全增量partialincrement偏增量partialderivative偏导数partialderivativeoff(x,y)withrespecttox(y)f(x,y)关于xy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implicitdifferentiat

17、ion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

18、小值extremevalue最值absolutemaximum(minimum)最大最小值交换积分秩序polarcoordinates极坐标doubleintegralsinpolarcoordinates极坐标下的二重积分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volume体积lamina平面薄片mass质量density密度momentaboutx-axis关于x轴的静力矩centerofmass重心o

19、bjectivefunction目标函数constraint约束条件momentofinertia转动惯量surface曲面methodofleastsquare最/、二areaofasurface曲面的面积乘法triple integral 三重积分rectangle 矩形rectangular coordinates 直角坐标系cylinder 柱面cylindrical coordinates 柱面坐标系sphere 球面spherical coordinates 球面坐标系change of variables in multipleintegrals 重积分的变量替换Jacobian

20、 determinant 雅可比行列式line integral 曲线积分line integral with respect to arclength 对弧长的曲线积分第一型line integral with respect to x ( y )对坐标x y 曲线积分 第二型line integral of a vector field向量场的曲线积分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multipleintegral重积分doubleintegral二重积分iteratedintegral累次积分region区域regionofintegration积分区域typeX(Y)regionXY型区域orderofintegration积分秩序reversetheorderofintegrationsmoothcurve光滑曲线piecewisesmoothcu