微積分雙語詞匯

1、irrational number 無理數(shù) negative number 負(fù)數(shù) mapping 映射寸function 函數(shù)increasing function 土曾函數(shù) bounded function 有界函數(shù) even function 偶函數(shù) composite function 復(fù)合函數(shù) domain 定義域 range 值域 dependent variable 因變量 divergent sequence 發(fā)散數(shù)歹U decreasing sequence 遞減數(shù)歹Ilimit 極限 one-sided limit 單側(cè)極限 The Squeeze Theorem 夾逼定理

2、equivalent infinitesimal order of infinitesimalincrement 曾量f(x) is continuous at x discontinuity 間斷點(diǎn) removable discontinuity infinite discontinuityintermediate value zero point 零點(diǎn) equation 方程MATHEMATICAL TERMS (Part 1)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

3、解x X for all x Xformula 公式if and only if ( iff )當(dāng)且僅當(dāng)x X there exists an x Xsuch that 使得given 已矢口set集合finite set有限集infinite set 無限集interval 區(qū)間open interval 開區(qū)間closed interval 閉區(qū)間neighborhood 鄰域number 數(shù)natural number 自然數(shù)integer 整數(shù)odd number 奇數(shù)even number 偶數(shù)real number 實(shí)數(shù)rational number 有理數(shù)positive num

4、ber 正數(shù)monotone function 單調(diào)函數(shù)decreasing function 減函數(shù)odd function 奇函數(shù)periodic function 周期函數(shù)inverse function 反函數(shù)variable 變量 independent variable 自變量sequence 數(shù)歹|convergent sequence 收斂數(shù)歹Ibounded sequence 有界數(shù)歹Iincreasing sequence 遞增數(shù)歹Ileft-hand limit 左極限 right-hand limit 右極限 infinity 無窮大infinitesimal 無窮小等

5、價(jià)無窮小 infinitesimal of higher order高階無窮小無窮小的階infinitesimals of the same order 同階無窮小continuous function 連續(xù)函數(shù) continuity連續(xù)性在 x 連續(xù)f(x) is discontinuous at x 在 x 間斷discontinuity of the first (second) kind 第一(二)類間斷點(diǎn)可去間斷點(diǎn) jump discontinuity跳躍間斷點(diǎn)無窮間斷點(diǎn)介值 The Intermediate Value Theorem 介值定理The Zero Point Theo

6、rem 零點(diǎn)定理root 根uniform continuity 一致連續(xù)derivative 導(dǎo)數(shù)rate of change 變化率 velocity 速度instantaneous velocity 瞬時(shí)速度tangent (line)切線 normal (line)法線slope 斜率left-hand derivative 左導(dǎo)數(shù) right-hand derivative 右導(dǎo)數(shù)f(x) is differentiable at x f(x)在 x 處可導(dǎo)(可微)differentiation 求導(dǎo)The Chain Rule 鏈?zhǔn)椒ㄘ?differentiation formul

7、as 求導(dǎo)公式implicit function 隱函數(shù)explicit function 顯函數(shù)implicit differentiation 隱函數(shù)求導(dǎo)logarithm 對數(shù)Logarithmic differentiation 對數(shù)求導(dǎo)法parameter 參數(shù)parametric equation 參數(shù)方程parametric curve 參數(shù)曲線hyperbolic function 雙曲函數(shù)hyperbolic sine 雙 曲正弦hyperbolic cosine 雙 曲余弦hyperbolic tangent 雙 曲正切Taylor polynomial 泰勒多項(xiàng)式hype

8、rbolic cotangent 雙曲余切MATHEMATICAL TERMS (Part 2)differential微分differential quotient微商approximate value近似值error誤差relative error相對誤差absolute error絕對誤差invariance of differential form微分形式不變性 higher derivative高階導(dǎo)數(shù)first derivative一階導(dǎo)數(shù)second derivative二階導(dǎo)數(shù)third derivative三階導(dǎo)數(shù)nth derivativen階導(dǎo)數(shù)twice differe

9、ntiable二階可導(dǎo)acceleration加速度mean value中值The Mean Value Theorem中值定理Rolle s Theorem羅爾定理Lagranges Mean Value Theorem 拉格朗日中值定理Cauchy s Mean Value Theorem柯西中值定理 equality等式inequality不等式indeterminate form 不定型 (未定式)indeterminate form of type ()()型未定式L Hospital, s Rule 洛必達(dá)法則Taylor s formula 泰勒公式polynomial多項(xiàng)式nt

10、h-degree polynomial n 次多項(xiàng)式remaind余項(xiàng)Lagrange s form of remainder拉格朗日型余項(xiàng)Peano s form of remainder皮亞諾型余項(xiàng)accuracy精確度margin邊際marginal cost邊際成本marginalrevenue邊際收益elasticity彈性density密度mass質(zhì)量extreme value極值Maclaurin formula 麥克勞林公式Mauclaurin polynomial麥克勞林多項(xiàng)式polynomial approximation 多項(xiàng)式逼近local maximum value極

11、大值local minimum value 極小值(absolute) maximum最大值(absolute) minimum最小值stationary point 駐點(diǎn)（穩(wěn)定點(diǎn)）critical point臨界點(diǎn)The First (Second) Derivative Test（極值的）一（二）階判別法convex凸的convex curve凸曲線concave凹的concave curve凹曲線convex function凸函數(shù)point of inflection拐點(diǎn)asymptote漸近線horizontal asymptote水平漸近線vertical asymptote垂直漸

12、近線slant asymptote斜漸近線curve sketching作圖sketch a curve作圖curvature曲率The bisection method二分法The secant method弦位法Newton s method牛頓（切線）法The tangent method切線法differential calculus微分學(xué)integral積分integral calculus積分學(xué)definite integral定積分indefinite integral不定積分partition分割Riemann sum黎曼和integral sign積分符號integrand被

13、積函數(shù)upper (lower) limit of integration 積分上(下)限integration積分（求積）integrable可積的f(x) is integrable ona, bintegrable function可積函數(shù)integrability可積性sufficient condition充分條件necessary condition必要條件piecewise continuous分段連續(xù)property性質(zhì)The mean value theorem of integral 積分中值定理The fundamental theorem of calculus微積分基

14、本定理Newton-Leibniz formula primitive function (anti-derivative) 原函數(shù)(反導(dǎo)數(shù))The substitution rule for integration 換兀積分法The inverse of the chain rule 反鏈?zhǔn)椒?湊微分法)integration by parts fraction partial fraction分部積分法rational function 有理函數(shù)分式 irreducible fraction最簡分式vector 矢量 magnitude of a vector dot product 點(diǎn)積

15、 a is perpendicular (orthogonal) to b coordinate system 坐標(biāo)系 x-axis x 軸 direction angle 方向角MATHEMATICAL TERMS (Part 3) free vector 矢量的模unit vectorvector producta與b垂直coordinate axis自由矢量單位矢量矢量積coordinate坐標(biāo)軸zero vector scalar product cross product坐標(biāo)零矢量數(shù)量積 叉積coordinate plane 坐標(biāo)面 direction cosine 方向余弦 oct

16、ant圭卜限r(nóng)ectangular coordinate system 直角坐標(biāo)系 the first octant 第一卦限variable 變量function of two (three) variables 二(三)元函數(shù) independent variable 自變量 domain定義域 set of points 點(diǎn)集 interior point 內(nèi)點(diǎn) open set 開集 region 區(qū)域 open region 開區(qū)域 closed region 閉區(qū)域 bounded region 有界區(qū)域 unbounded region 無界區(qū)域 cluster point 聚點(diǎn)

17、 double limit 二重極限 iterated limit 累次極限 continuity 連續(xù)性 increment 增量 total increment 全增量 partial increment 偏增量 partial derivative 偏導(dǎo)數(shù)partial derivative of f(x,y) with respect to x ( y ) f(x,y)關(guān)于 x (y) 的偏導(dǎo)數(shù) higher partial derivative 高階偏導(dǎo)數(shù)mixed partial derivative混合偏導(dǎo)數(shù)Laplace equation 拉普拉斯方程total differe

18、ntial 全微分function of several variables dependent variable 因變量range值域neighborhood 鄰域boundary point 邊界點(diǎn) bound 邊界 closed set 閉集 connected set 連通集多元函數(shù)部分分式partial fraction decomposition部分分式分解differentiable 可微 implicit differentiation curve曲線 tangent line 切線 normal vector 法矢 sphere球面 directional derivativ

19、e Nf delf local extremum 極值 extreme value 最值implicit function 隱函數(shù)Jacobian determinant雅可比行列式tangent vector 切矢surface 曲面tangent plane 切平面chain rule鏈?zhǔn)椒▌t 隱函數(shù)微分法cone錐面gradient 梯度 gradient vector 梯度矢量等值線 level surface等值面極大值 local minimum極小值最大（最?。┲祍pace curve空間曲線 normal plane 法平面 normal line 法線 cylinder 柱面

20、方向?qū)?shù)level curvelocal maximumabsolute maximum （minimum） stationary point （critical point） 駐點(diǎn)（臨界點(diǎn)） conditional extremum條件極值Lagrange multiplier 拉格朗日乘數(shù)method of Lagrange multiplier 拉格朗日乘數(shù)法 objective function 目標(biāo)函數(shù) constraint 約束條件 method of least square最小二乘法field 場 scalar field 數(shù)量場 vector field 矢量場 gradie

21、nt field 梯度場 potential field 勢場 potential function 勢函數(shù) conservative field 保守場 gravitational field 引力場 force field 力場 velocity field 速度場MATHEMATICAL TERMS（Part 4）multiple integral 重積分 double integral 二重積分iterated integral 累次積分region 區(qū)域 region of integration 積分區(qū)域type X （Y） region X （Y） 型區(qū)域order of int

22、egration 積分秩序 reverse the order of integration交換積分秩序polar coordinates 極坐標(biāo) double integrals in polar coordinates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 moment about x-axis 關(guān)于 x 軸的（靜）力矩 center of mass 重心 moment of inertia 轉(zhuǎn)動慣量surface 曲面 area of a surface 曲面的面積 triple integral 三重積分 rectangle 矩形 r

23、ectangular coordinates 直角坐標(biāo)系cylinder 柱面cylindrical coordinates 柱面坐標(biāo)系 sphere 球面 spherical coordinates 球面坐標(biāo)系change of variables in multiple integrals重積分的變量替換Jacobian determinant雅可比行列式line integral 曲線積分line integral with respect to arc length對弧長的曲線積分（第一型）line integral with respect to x （ y ） 對坐標(biāo) x（y）曲線積分（第二型）line integral of a vector field 向量場的曲線積分 smooth curve 光滑曲線 piecewise smooth curve 逐段光滑曲線o