微積分英文專業(yè)詞匯

1、微積分詞匯第一章函數(shù)與極限ChapterlFunction and Limit集合set元素 element子集subset 空集 empty set 并集union 交集 intersection 差集 difference of set 基本集basic set 補集 complement set 直積 direct product 笛卡兒積 Cartesian product 開區(qū)間 open interval 閉區(qū)間 closed interval 半開區(qū)間 half open interval 有限區(qū)間 finite interval 區(qū)間的長度 length of an inter

2、val 無限區(qū)間 infinite interval 領(lǐng)域 neighborhood領(lǐng)域的中心 centre of a neighborhood 領(lǐng)域的半徑 radius of a neighborhood 左領(lǐng)域 left neighborhood 右領(lǐng)域 right neighborhood 映射 mappingX 到 Y 的映射 mapping of X ontoY 滿射 surjection 單射 injection 一一映射 one-to-one mapping 雙射 bijection 算子 operator 變化 transformation 函數(shù) function 逆映射 in

3、verse mapping 復(fù)合映射 composite mapping 自變量 independent variable 因變量 dependent variable 定義域domain函數(shù)值 value of function 函數(shù)關(guān)系 function relation 值域 range自然定義域natural domain 單值函數(shù) single valued function 多值函數(shù) multiple valued function 單值分支 one-valued branch 函數(shù)圖形 graph of a function 絕對值函數(shù)absolute value 符號函數(shù)sig

4、h function 整數(shù)部分integral part 階梯曲線step curve 當(dāng)且僅當(dāng) if and only if(iff) 分段函數(shù) piecewise function 上界 upper bound 下界 lower bound 有界 boundedness 無界 unbounded函數(shù)的單調(diào)性 monotonicity of a function 單調(diào)增加的increasing 單調(diào)減少的decreasing單調(diào)函數(shù) monotone function函數(shù)的奇偶性 parity(odevity) of a function 對稱 symmetry偶函數(shù) even functi

5、on 奇函數(shù) odd function 函數(shù)的周期性 periodicity of a function 周期period反函數(shù) inverse function 直接函數(shù) direct function 復(fù)合函數(shù) composite function 中間變量 intermediate variable 函數(shù)的運算 operation of function 基本初等函數(shù) basic elementary function 初等函數(shù) elementary function 冪函數(shù) power function指數(shù)函數(shù) exponential function 對數(shù)函數(shù) logarithmic

6、 function 三角函數(shù) trigonometric function 反三角函數(shù) inverse trigonometric function 常數(shù)函數(shù) constant function 雙曲函數(shù) hyperbolic function 雙曲正弦 hyperbolic sine 雙曲余弦 hyperbolic cosine 雙曲正切 hyperbolic tangent 反雙曲正弦 inverse hyperbolic sine 反雙曲余弦 inverse hyperbolic cosine 反雙曲正切 inverse hyperbolic tangent極限limit數(shù)列 seque

7、nce of number收斂 convergence收斂于 a converge to a 發(fā)散 divergent極限的唯一性 uniqueness of limits 收斂數(shù)列的有界性 boundedness of a convergent sequence子列 subsequence函數(shù)的極限 limits of functions函數(shù) 當(dāng)x趨于x0時的極限limit of functions as x approaches x0左極限left limit右極限 right limit單側(cè)極限 one-sided limits水平漸近線 horizontal asymptote無窮小

8、infinitesimal無窮大infinity鉛直漸近線 vertical asymptote 夾逼準(zhǔn)則squeeze rule單調(diào)數(shù)列 monotonic sequence高階無窮小 infinitesimal of higher order 低階無窮小 infinitesimal of lower order 同階無窮小 infinitesimal of the same order作者：新少年特工2007-10-8 18:37 回復(fù)此發(fā)言2高等數(shù)學(xué)-翻譯等階無窮小 equivalent infinitesimal函數(shù)的連續(xù)性 continuity of a function增量 inc

9、rement函數(shù) 在 x0 連續(xù) the function is continuous at x0左連續(xù) left continuous右連續(xù) right continuous區(qū)間上的連續(xù)函數(shù)continuous function 函數(shù) 在該區(qū)間上連續(xù) function is continuous on an interval不連續(xù)點 discontinuity point第一類間斷點 discontinuity point of the first kind第二類 間斷點 discontinuity point of the second kind初等函數(shù)的連續(xù)性 continuity of

10、 the elementary functions定義區(qū)間 defined interval最大值global maximum value (absolute maximum)最小值global minimum value (absolute minimum)零點定理 the zero point theorem 介值定理 intermediate value theorem第二章導(dǎo)數(shù)與微分Chapter2Derivative and Differential速度 velocity勻速運動 uniform motion 平均速度 average velocity 瞬時速度 instantane

11、ous velocity 圓的切線 tangent line of a circle 切線 tangent line切線的斜率 slope of the tangent line 位置函數(shù) position function 導(dǎo)數(shù) derivative可導(dǎo) derivable函數(shù)的變化率問題problem of the change rate of a function導(dǎo)函數(shù) derived function左導(dǎo)數(shù) left-hand derivative 右導(dǎo)數(shù) right-hand derivative 單側(cè)導(dǎo)數(shù) one-sided derivatives在閉區(qū)間【a,b】上可導(dǎo)is de

12、rivable on the closed interval a,b切線方程 tangent equation 角速度 angular velocity 成本函數(shù)cost function 邊際成本marginal cost 鏈?zhǔn)椒▌tchain rule 隱函數(shù) implicit function 顯函數(shù) explicit function 二階函數(shù) second derivative 三階導(dǎo)數(shù) third derivative高階導(dǎo)數(shù) nth derivative 萊布尼茨公式 Leibniz formula 對數(shù)求導(dǎo)法log- derivative 參數(shù)方程 parametric equa

13、tion 相關(guān)變化率 correlative change rata 微分 differential 可微的 differentiable 函數(shù)的微分 differential of function 自變量的微分 differential of independent variable微商 differential quotient間接測量誤差 indirect measurement error 絕對誤差absolute error 相對誤差 relative error第三章微分中值定理與導(dǎo)數(shù)的應(yīng)用Chapter3MeanValue Theorem of Differentials an

14、d the Application of Derivatives羅馬定理 Rolle s theorem 費馬弓I理 Fermat s lemma 拉格朗日中值定理Lagrange s mean value theorem駐點 stationary point穩(wěn)定點 stable point臨界點 critical point輔助函數(shù) auxiliary function拉格朗日中值公式Lagrange s mean value formula柯西中值定理Cauchy s mean value theorem洛必達法則 L Hospital s Rule 0/0 型不定式 indetermin

15、ate form of type 0/0 不定式 indeterminate form泰勒中值定理Taylor s mean value theorem 泰勒公式 Taylor formula 余項 remainder term拉格朗 日余項 Lagrange remainder term 麥克勞林公式 Maclaurin s formula 佩亞諾公式 Peano remainder term 凹凸，性 concavity凹向上的 concave upward, cancave up 凹向下的，向上凸的 concave downward concave down拐點 inflection p

16、oint函數(shù)的極值 extremum of function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(biāo)函數(shù) objective function曲率 curvature弧微分 arc differential平均曲率 average curvature曲率園 circle of curvature曲率中心 center of curvature曲率半徑 radius of curvature漸屈線evolute漸伸線

17、involute根的隔離 isolation of root隔離區(qū)間 isolation interval切線法 tangent line method第四章不定積分Chapter4Indefinite Integrals原函數(shù) primitive function(antiderivative) 積分號 sign of integration被積函數(shù)integrand積分變量 integral variable積分曲線 integral curve積分表 table of integrals換元積分法 integration by substitution分部積分法 integration

18、by parts分部積分公式 formula of integration by parts有理函數(shù) rational function真分式 proper fraction假分式 improper fraction第五章定積分Chapters Definite Integrals曲邊梯形 trapezoid with曲邊 curve edge窄矩形 narrow rectangle曲 邊梯形 的面積 area of trapezoid withcurved edge積分下限 lower limit of integral積分上限 upper limit of integral積分區(qū)間 int

19、egral interval分害。partition積分和 integral sum可積 integrable矩形法 rectangle method積分中值定理 mean value theorem of integrals函數(shù)在區(qū)間上的平均值average value of a function on an integvals牛頓一萊布尼茨公式 Newton-Leibniz formula微積分基本公式fundamental formula of calculus換元公 式 formula for integration by substitution遞推公式 recurrence for

20、mula反常積分 improper integral反 常積分 發(fā) 散 the improper integral is divergent反 常積 分收斂 the improper integral is convergent無窮限的反常積分 improper integral on an infinite interval無界函數(shù)的反常積分improper integral of unbounded functions絕對收斂 absolutely convergent第六章定積分的應(yīng)用Chapter6 Applications of the Definite Integrals元素法 t

21、he element method面積元素 element of area平面圖形的面積area of a luane figure直角坐標(biāo)又稱“笛卡兒坐標(biāo)(Cartesian coordinates) ”極坐標(biāo) polar coordinates拋物線parabola橢圓 ellipse旋轉(zhuǎn)體的面積 volume of a solid of rotation旋轉(zhuǎn)橢球體 ellipsoid of revolution, ellipsoid of rotation曲線的弧長 arc length of acurve可求長的rectifiable光滑smooth功 work水壓力 water pr

22、essure弓|力 gravitation變力 variable force第七章空間解析幾何與向量代數(shù)Chapter? Space Analytic Geometry and Vector Algebra向量vector自 由向量 free vector單位向量 unit vector零向量 zero vector相等equal平行 parallel向量的線性運算 linear poeration of vector三角法貝9 triangle rule平行四邊形法則parallelogram rule交換律 commutative law結(jié)合律 associative law負(fù)向量 neg

23、ative vector差 difference分配律 distributive law空間直角坐標(biāo)系 space rectangular coordinates坐標(biāo)面 coordinate plane圭卜限octant向量的模 modulus of vector向量 a 與 b 的夾角 angle between vector a and b方向余弦 direction cosine方向角 direction angle向量在軸上的投影 projection of a vector onto an axis數(shù)量積，外積，叉積scalar product,dot product,inner p

24、roduct曲面方程 equation for a surface球面 sphere旋轉(zhuǎn)曲面 surface of revolution母線 generating line軸 axis圓錐面cone頂點vertex旋轉(zhuǎn)單葉雙曲面 revolution hyperboloids of one sheet旋轉(zhuǎn)雙葉雙曲面 revolution hyperboloids oftwo sheets柱面 cylindrical surface ,cylinder 圓柱面 cylindrical surface 準(zhǔn)線 directrix拋物柱面 parabolic cylinder二次曲面 quadric

25、surface 橢圓錐面dlliptic cone 橢球面ellipsoid單葉雙曲面 hyperboloid of one sheet 雙葉雙曲面 hyperboloid of two sheets 旋轉(zhuǎn)橢球面 ellipsoid of revolution 橢圓拋物面 elliptic paraboloid 旋轉(zhuǎn)拋物面 paraboloid of revolution 雙曲拋物面 hyperbolic paraboloid 馬鞍面 saddle surface橢圓柱面 elliptic cylinder雙曲柱面 hyperbolic cylinder拋物柱面 parabolic cylin

26、der 空間曲線space curve空間曲線的一般方程general form equations of a space curve空間曲線的參數(shù)方程 parametric equations of a space curve螺轉(zhuǎn)線spiral螺矩pitch投影柱面 projecting cylinder投影 projection平面的點法式方程 pointnorm form eqyation of a plane法向量 normal vector平面的一般方程 general form equation of a plane兩平面的夾角 angle between two planes 點

27、到平面的距離 distance from a point to a plane空間直線的一般方程general equation of a line in space方向向量 direction vector直線的點向式方程 pointdirection form equations of a line方向數(shù) direction number直線的參數(shù)方程 parametric equations of a line兩直線的夾角 angle between two lines垂直 perpendicular直線與平面的夾角angle between a line and a planes平面束

28、 pencil of planes平面束的方程 equation of a pencil of planes行列式 determinant 系數(shù)行列式 coefficient determinant第八章多元函數(shù)微分法及其應(yīng)用Chapters Differentiation of Functions of Several Variables and Its Application 一元函數(shù) function of one variable 多元函數(shù) function of several variables 內(nèi)點 interior point 夕卜點 exterior point邊界點 fro

29、ntier point,boundary point 聚點 point of accumulation 開集 openset 閉集 closed set 連通集 connected set 開區(qū)域 open region 閉區(qū)域 closed region 有界集 bounded set 無界集 unbounded set n 維空間 n-dimentional space 二重極限 double limit多元函數(shù)的連續(xù)性continuity of function of seveal連續(xù)函數(shù) continuous function 不連續(xù)點 discontinuity point 一致連續(xù)

30、 uniformly continuous 偏導(dǎo)數(shù) partial derivative 對自變量x的偏導(dǎo)數(shù)partial derivative with respect to independent variable x高階偏導(dǎo)數(shù) partial derivative of higher order 二階偏導(dǎo)數(shù) second order partial derivative 混合偏導(dǎo)數(shù) hybrid partial derivative 全微分 total differential 偏增量 oartial increment 偏微分 partial differential 全增量 tota

31、l increment 可微分 differentiable必要條件 necessary condition 充分條件 sufficient condition 疊加原理 superpostition principle 全導(dǎo)數(shù) total derivative中間變量 intermediate variable隱函數(shù)存在定理 theorem of the existence of implicit function曲線的切向量 tangent vector of a curve 法平面 normal plane向量方程 vector equation向量值函數(shù) vector-valued f

32、unction 切平面 tangent plane法線 normal line方向?qū)?shù) directional derivative梯度 gradient數(shù)量場 scalar field 梯度場 gradient field 向量場 vector field 勢場 potential field 弓I力場 gravitational field 引力勢 gravitational potential 曲面在一點的切平面tangent plane to asurface at a point曲線在一點的法線 normal line to a surface at a point無條件極值 unc

33、onditional extreme values 條件極值 conditional extreme values 拉格朗日乘數(shù)法 Lagrange multiplier method 拉格朗日乘子Lagrange multiplier 經(jīng)驗公式 empirical formula最小二乘法 method of least squares 均方誤差 mean square error第九章重積分Chapter9Multiple Integrals二重積分 double integral 可加性 additivity累次積分 iterated integral體積元素 volume elemen

34、t 三重積分 triple integral 直角坐標(biāo)系中的體積元素 volume element in rectangular coordinate system柱面坐標(biāo) cylindrical coordinates柱面坐標(biāo)系中的體積元素 volume element in cylindrical coordinate system球面坐標(biāo) spherical coordinates球面坐標(biāo)系中的體積元素 volume element in spherical coordinate system反常二重積分 improper double integral曲面的面積 area of a s

35、urface質(zhì)心 centre of mass靜矩 static moment密度 density形心 centroid轉(zhuǎn)動慣量 moment of inertia參變量 parametric variable第十章曲線積分與曲面積分Chapter10Line(Curve)Integrals and Surface Integrals對弧長的曲線積分line integrals with respect to arc hength第一類曲線積分 line integrals of the first type對坐標(biāo)的曲線積分 line integrals with respect to x,y

36、,and z第二類曲線積分 line integrals of the second type有向曲線弧directed arc單連通區(qū)域 simple connected region復(fù)連通區(qū)域 complex connected region格林公式Green formula第一類曲面積分 surface integrals of the first type對面的曲面積分 surface integrals with respect to area有向曲面 directed surface對坐標(biāo)的曲面積分 surface integrals with respect to coordin

37、ate elements第二類曲 面積分 surface integrals of the second type有向曲面元 element of directed surface高斯公式 gauss formula拉普拉斯算子Laplace operator格林第一公式 Green s first formula通量 flux散度 divergence斯托克斯公式Stokes formula環(huán)流量 circulation旋度 rotation,curl第十一章無窮級數(shù)ChapterllInfinite Series一般項 general term 部分和 partial sum 余項 rem

38、ainder term 等比級數(shù) geometric series 幾何級數(shù) geometric series 公比 common ratio 調(diào)和級數(shù) harmonic series 柯西收斂準(zhǔn)則 Cauchy convergence criteria, Cauchy criteria for convergence 正項級數(shù) series of positive terms 達朗貝爾判別法D Alembert test 柯西判別法Cauchy test 交錯級數(shù) alternating series 絕對收斂 absolutely convergent 條件收斂 conditionally

39、 convergent 柯西乘積 Cauchy product 函數(shù)項級數(shù) series of functions 發(fā)散點 point of divergence 收斂點 point of convergence 收斂域 convergence domain 和函數(shù) sum function 冪級數(shù) power series冪級數(shù)的系數(shù) coeffcients of power series 阿貝爾定理 Abel Theorem 收斂半徑 radius of convergence 收斂區(qū)間 interval of convergence 泰勒級數(shù)Taylor series 麥克勞林級數(shù) Ma

40、claurin series 二項展開式 binomial expansion 近似計算 approximate calculation 舍入誤差 round-off error,rounding error 歐拉公式 Euler s formula魏爾斯特拉絲判別法Weierstrass test 三角級數(shù) trigonometric series 振幅 amplitude角頻率 angular frequency 初相 initial phase 矩形波 square wave 諧波分析 harmonic analysis 直流分量 direct component基波 fundament

41、al wave二次諧波 second harmonic三角函數(shù)系 trigonometric function system 傅立葉系數(shù) Fourier coefficient傅立葉級數(shù)Forrier series周期延拓 periodic prolongation正弦級數(shù)sine series余弦級數(shù)cosine series奇延拓 odd prolongation偶延拓 even prolongation傅立葉級數(shù)的復(fù)數(shù)形式 complex form of Fourier series第十二章微分方程Chapter12Differential Equation解微分方程 solve a d

42、irrerential equation 常微分方程 ordinary differential equation 偏微分方程 partial differential equation,PDE 微分方程的階 order of a differential equation 微分方程的解 solution of a differential equation微分方程的通解 general solution of a differential equation初始條件 initial condition微分方程的特解 particular solution of a differential equation初值問題 initial value problem微分方程的積分曲線integral curve of adifferential equation可分離變量的微分方程 variable separable differential equation隱式解 implicit