MATHEMATICALTERMS(Part1)calculus微積分definition定義theorem定理lemma引理corollary推論prove證明proof證明show證明solution解formula公式ifandonlyif(iff)當且僅當xXforallxXxXthereexistsanxXsuchthat使得given已知set集合finiteset有限集infiniteset無限集interval區間openinterval開區間closedinterval閉區間neighborhood鄰域number數naturalnumber自然數integer整數oddnumber奇數evennumber偶數realnumber實數rationalnumber有理數irrationalnumber無理數positivenumber正數negativenumber負數mapping映射function函數monotonefunction單調函數increasingfunction增函數decreasingfunction減函數boundedfunction有界函數oddfunction奇函數evenfunction偶函數periodicfunction周期函數compositefunction復合函數inversefunction反函數domain定義域range值域variable變量independentvariable自變量dependentvariable因變量sequence數列convergentsequence收斂數列divergentsequence發散數列boundedsequence有界數列decreasingsequence遞減數列increasingsequence遞增數列limit極限one-sidedlimit單側極限left-handlimit左極限right-handlimit右極限TheSqueezeTheorem夾擠定理infinity無窮大infinitesimal無窮小equivalentinfinitesimal等價無窮小infinitesimalofhigherorder高階無窮小orderofinfinitesimal無窮小的階infinitesimalsofthesameorder同階無窮小increment增量continuousfunction連續函數continuity連續性f(x)iscontinuousatx在x連續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derivative導數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左導數right-handderivative右導數f(x)isdifferentiableatxf(x)在x處可導(可微)differentiation求導TheChainRule鏈式法則differentiationformulas求導公式implicitfunction隱函數explicitfunction顯函數implicitdifferentiation隱函數求導logarithm對數Logarithmicdifferentiation對數求導法parameter參數parametricequation參數方程parametriccurve參數曲線hyperbolicfunction雙曲函數hyperbolicsine雙曲正弦hyperboliccosine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高階導數firstderivative一階導數secondderivative二階導數thirdderivative三階導數nthderivativen階導數twicedifferentiable二階可導acceleration加速度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洛必達法則Taylor’sformula泰勒公式polynomial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邊際成本marginalrevenue邊際收益elasticity彈性density密度mass質量extremevalue極值localmaximumvalue極大值localminimumvalue極小值(absolute)maximum最大值(absolute)minimum最小值stationarypoint駐點（穩定點）criticalpoint臨界點TheFirst(Second)DerivativeTest（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pointofinflection拐點asymptote漸近線horizontalasymptote水平漸近線verticalasymptote垂直漸近線slantasymptote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integral積分integralcalculus積分學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upper(lower)limitofintegration積分上（下）限integration積分（求積）integrable可積的f(x)isintegrableon[a,b]integrablefunction可積函數integrability可積性sufficientcondition充分條件necessarycondition必要條件piecewisecontinuous分段連續property性質Themeanvaluetheoremofintegral積分中值定理Thefundamentaltheoremofcalculus微積分基本定理Newton-Leibnizformulaprimitivefunction(anti-derivative)原函數（反導數）Thesubstitutionruleforintegration換元積分法Theinverseofthechainrule反鏈式法（湊微分法）integrationbyparts分部積分法rationalfunction有理函數fraction分式irreduciblefraction最簡分式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單位矢量scalarproduct數量積dotproduct點積vectorproduct矢量積crossproduct叉積aisperpendicular(orthogonal)toba與b垂直coordinate坐標coordinatesystem坐標系coordinateaxis坐標軸x-axisx軸coordinateplane坐標面directionangle方向角directioncosine方向余弦rectangularcoordinatesystem直角坐標系octant卦限thefirstoctant第一卦限variable變量functionoftwo(three)variables二（三）元函數functionofseveralvariables多元函數independentvariable自變量dependentvariable因變量domain定義域range值域setofpoints點集neighborhood鄰域interiorpoint內點boundarypoint邊界點bound邊界openset開集closedset閉集connectedset連通集region區域openregion開區域closedregion閉區域boundedregion有界區域unboundedregion無界區域clusterpoint聚點doublelimit二重極限iteratedlimit累次極限continuity連續性increment增量totalincrement全增量partialincrement偏增量partialderivative偏導數partialderivativeoff(x,y)withrespecttox(y)f(x,y)關于x（y）的偏導數higherpartialderivative高階偏導數mixedpartialderivative混合偏導數Laplaceequation拉普拉斯方程totaldifferential全微分differentiable可微chainrule鏈式法則implicitfunction隱函數implicitdifferentiation隱函數微分法Jacobiandeterminant雅可比行列式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方向導數gradient梯度gradientvector梯度矢量fdelflevelcurve等值線levelsurface等值面localextremum極值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methodofLagrangemultiplier拉格朗日乘數法objectivefunction目標函數constraint約束條件methodofleastsquare最小二乘法field場scalarfield數量場vectorfield矢量場gradientfield梯度場potentialfield勢場potentialfunction勢函數conservativefield保守場gravitationalfield引力場forcefield力場velocityfield速度場MATHEMATICALTERMS(Part4)multipleintegral重積分doubleintegral二重積分iteratedintegral累次積分region區域regionofintegration積分區域typeX(Y)regionX（Y）型區域orderofintegration積分秩序reversetheorderofintegration交換積分秩序polarcoordinates極坐標doubleintegralsinpolarcoordinates極坐標下的二重積分volume體積lamina平面薄片mass質量density密度momentaboutx-axis關于x軸的（靜）力矩centerofmass重心momentofinertia轉動慣量surface曲面areaofasurface曲面的面積tripleintegral三重積分rectangle矩形rectangularcoordinates直角坐標系cylinder柱面cylindricalcoordinates柱面坐標系sphere球面sphericalcoordinates球面坐標系changeofvariablesinmultipleintegrals重積分的變量替換Jacobiandeterminant雅可比行列式lineintegral曲線積分lineintegralwithrespecttoarclength對弧長的曲線積分（第一型）lineintegralwithrespecttox(y)對坐標x（y）曲線積分（第二型）lineintegralofavectorfield向量場的曲線積分smoothcurve光滑曲線piecewisesmoothcurve逐