(完整word)數(shù)學(xué)英文詞匯大全匯總,推薦文檔

1、微積分第一章函數(shù)與極限Chapterl Function 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(bǔ)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 interval無限區(qū)間 inf

2、inite 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 至ij Y 的映射 mapping of X ontoY滿射 surjection單射 injection映射 one-to-one mapping雙射 bijection算子 operator變化 transformation函數(shù) function逆映射 inverse mapping復(fù)合映射 composi

3、te 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) sigh function 整數(shù)部分 integral par

4、t 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 function 奇函數(shù) odd function 函數(shù)的

5、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(yùn)算 operation of function 基本初等函數(shù) basic elementary function 初等函數(shù) elementary function 哥函數(shù) power function 指數(shù)函數(shù) exponential function 對數(shù)函數(shù) logaAthmic function 三角函數(shù) trigon

6、ometric 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)歹U sequence of number收斂 convergen

7、ce收斂于 a converge to a發(fā)散 divergent極限的唯性uniqueness of limits收斂數(shù)歹 U 的有界性boundedness of a convergent sequence子歹U 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 infinitesimal無窮大 infi

8、nity鉛直漸近線 vertical asymptote夾逼準(zhǔn)貝U squeeze rule單調(diào)數(shù)歹 U monotonic sequence高階無窮/J、 infinitesimal of higher order彳氐階無窮小 infinitesimal of lower order同階無窮/J、 infinitesimal of the same order2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 increment函數(shù) 在 x0 連續(xù) the function is continuous

9、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(diǎn) discontinuity point第類間斷點(diǎn) discontinuity point of the first kind第二類間斷點(diǎn) discontinuity point of the second kind初等函數(shù)的連續(xù)性 continuity of the elementary functions定義區(qū)間 defined interval最大

10、值 global maximum value (absolute maximum)最小值 global minimum value (absolute minimum)零點(diǎn)定理 the zero point theorem介值定理 intermediate value theorem第二章導(dǎo)數(shù)與微分Chapter2 Derivative and Differential速度 velocity勻速運(yùn)動 uniform motion平均速度 average velocity瞬時速度 instantaneous velocity圓的切線 tangent line of a circle切線 tang

11、ent 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 derivable on the closed interval a,b切線方程 tangent equatio

12、n角速度 angular velocity成本函數(shù) cost function邊際成本 marginal cost鏈?zhǔn)椒▌t chain 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 equation相關(guān)變化率 correlative change rata微分 differential可微的 differentia

13、ble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Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 羅馬定理 Rolle' s theorem費(fèi)馬引理 Fermat

14、' s lemma拉格朗日中值定理Lagrange' s mean value theorem駐點(diǎn) stationary point穩(wěn)定點(diǎn) stable point臨界點(diǎn) 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(dá)法則 L' Hospital ' s Rule0/0 型不定式 indeterminate form of type 0/0不定式 indetermin

15、ate form泰勒中值定理Taylor' s mean value theorem泰勒公式 Taylor formula余項(xiàng) remainder term拉格朗 日余項(xiàng)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(diǎn) inflection point函數(shù)的極值 extremum of func

16、tion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involute根的隔離 isolation of

17、root隔離區(qū)間 isolation interval切線法 tangent line method第四章不定積分Chapter4 Indefinite 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分音 B 積分法 integration by parts分音 B 積分公式 form

18、ula 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Chapter5 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 with curved edge積分下限 lower limit of integral積分上限 upper limit of integral積分區(qū)間 integral interval分害U par

19、tition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 formula反常積分 improper integr

20、al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 the element method面積元素 element

21、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 pressure弓 I力 gravitation變力

22、 variable force第七章 空間解析幾何與向量代數(shù)Chapter7 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(yùn)算linear poeration of vector三角法貝 U 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 negative vector差 differen

23、ce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 product 曲面方程 equation

24、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(diǎn) vertex旋轉(zhuǎn)單葉雙曲面revolution hyperboloids of one sheet旋轉(zhuǎn)雙葉雙曲面revolution hyperboloids of two 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 surface橢圓錐面 dlliptic c

25、one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 cylinder空間曲線 space curve空間曲線的般方程ge

26、neral 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(diǎn)法式方程pointnorm form eqyation of a plane法向量 normal vector平面的般方程general form equation of a plane兩平面的夾角 angle between two planes點(diǎn)至 U平面的距離distance from a point to a

27、 plane空間直線的般方程general equation of a line in space方向向量 direction vector直線的點(diǎn)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 pencil of planes平面束的方程 equation of

28、 a pencil of planes行歹U式 determinant系數(shù)行歹U式 coefficient determinant第八章多元函數(shù)微分法及其應(yīng)用Chapter8 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(diǎn) interior point外點(diǎn) exterior point邊界點(diǎn) frontier point,boundary point聚點(diǎn) point of a

29、ccumulation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 setn 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(diǎn) discontinuity point一致連續(xù) uniformly continuous偏導(dǎo)數(shù) partial derivative對自變量 x 的

30、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 total increment可微分 differentiable必要條件 necessary condition充分條

31、件 sufficient condition疊力口原理 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 function切平面 tangent plane法線 normal line方向?qū)?shù) directional deriva

32、tive梯度 gradient數(shù)量場 scalar field梯度場 gradient field向量場 vector field勢場 potential field引力場 gravitational field弓 I力勢 gravitational potential曲面在點(diǎn)的切平面tangent plane to a surface at a point曲線在點(diǎn)的法線normal line to a surface at a point無條件極值 unconditional extreme values條件極值 conditional extreme values拉格朗 日乘數(shù)法 Lagr

33、ange multiplier method拉格朗日乘子 Lagrange multiplier經(jīng)驗(yàn)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Chapter9 Multiple Integrals二重積分 double integral可加性 additivity累次積分 iterated integral體積元素 volume element三重積分 triple integral直角坐標(biāo)系中的體積元素volume element in rectangular coordinate

34、 system柱面坐標(biāo) cylindrical coordinates柱面坐標(biāo)系中白體積元素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 surface質(zhì)心 centre of mass靜矩 static moment密度 density形心 centroid轉(zhuǎn)動慣量 moment of in

35、ertia參變量 parametric variable第十章曲線積分與曲面積分Chapter10 Line(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,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 c

36、onnected 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 coordinate elements第二類曲面積分surface integrals of the second type有向曲面元 element of directed

37、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)Chapter11 Infinite Series一般項(xiàng) general term部分和 partial sum余項(xiàng) remainder 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

38、 series柯西收斂準(zhǔn)貝 UCauchy convergence criteria, Cauchy criteria for convergence正項(xiàng)級數(shù) series of positive terms達(dá)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 convergent柯西乘積 Cauchy product函數(shù)項(xiàng)級數(shù) series of functions發(fā)散點(diǎn) point of divergence收斂點(diǎn) poi

39、nt of convergence收斂域 convergence domain和函數(shù) sum function哥級數(shù) power series哥級數(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) Maclaurin series二項(xiàng)展開式 binomial expansion近似計算 approximate calculation舍入誤差 round-off error,rounding err

40、or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 fundamental 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 ser

41、ies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Chapter12 Differential Equation解微分方程 solve a dirrerential equation常微分方程 ordinary differential equation偏微分方程 partial differential equation,PDE微分方程的階

42、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 a differential equation可分離變量的微分方程 variable separ

43、able differential equation 隱式解 implicit solution隱式通解 inplicit general solution衰變系數(shù) decay coefficient衰變decay齊次方程 homogeneous equation一階線性方程 linear differential equation of first order 非齊次 non-homogeneous齊次線性方程 homogeneous linear equation 非齊次線性方程non-homogeneous linear equation常數(shù)變易法 method of variation

44、 of constant暫態(tài)電流 transient stata current穩(wěn)態(tài)電流 steady state current伯努利方程 Bernoulli equation全微分方程 total differential equation積分因子 integrating factor高階微分方程differential equation of higher order懸鏈線 catenary高階線性微分方程linera differential equation of higher orderA自由振動的微分方程 強(qiáng)迫振動的微分方程 串聯(lián)電路的振蕩方程二階線性微分方程differenti

45、al equation of free vibration differential equation of forced oscillation oscillation equation of series circuitsecond order linera differential equation線性才目關(guān) linearly dependence線性無關(guān) linearly independceequation with二階常系數(shù)齊次線性微分方程second order homogeneour linear differential constant coefficient二階變系數(shù)齊次

46、線性微分方程second order homogeneous linear differential equation withvariable coefficient特征方程 characteristic equation無阻尼自 由振動的微分方程differential equation of free vibration with zero damping固有頻率 natural frequency簡諧振動 simple harmonic oscillation,simple harmonic vibration微分算子 differential operator待定系數(shù)法 method

47、 of undetermined coefficient共振現(xiàn)象 resonance phenomenon歐拉方程 Euler equation哥級數(shù)解法 power series solution數(shù)值解法 numerial solution勒讓德方程 Legendre equation微分方程組 system of differential equations常系數(shù)線性微分方程組system of linera differential equations with constant coefficient線性代數(shù)adjont(adjugate) of matrix A augmented

48、matrixBblock diagonal matrix block matrix basic solution setCCauchy-Schwarz inequality characteristic equation characteristic polynomial coffcient matrix cofactor cofactor expansion column vector commuting matrices consistent linear system Cramer' s rule Cross- product termDDeterminantDiagonal e

49、ntries Diagonal matrix Dimension of a vector space VEechelon matrix eigenspace eigenvalue eigenvector eigenvector basis elementary matrix elementary row operationsA的伴隨矩陣A的增廣矩陣塊對角矩陣塊矩陣基礎(chǔ)解系柯西-許瓦茲不等式特征方程特征多項(xiàng)式系數(shù)矩陣代數(shù)余子式代數(shù)余子式展開列向量交換矩陣相容線性方程組克萊姆法則交叉項(xiàng)行列式對角元素對角矩陣向量空間V的維數(shù)梯形矩陣特征空間特征值特征向量 特征向量的基 初等矩陣 行初等變換full

50、rank滿秩fundermental set of solution基礎(chǔ)解系Gcentergrneral solutionGram-Schmidt processHhomogeneous linear equationsIidentity matrixinconsistent linear system indefinite matrixindefinit quatratic form infinite-dimensional space inner productinverse of matrix ALlinear combination linearly dependent linearl

51、y independent linear transformation lower triangular matrixMmain diagonal of matrix A matrix通解施密特正交化過程齊次線性方程組單位矩陣不相容線性方程組不定矩陣不定二次型無限維空間內(nèi)積逆矩陣線性組合線性相關(guān)線性無關(guān)線性變換 下三角形矩陣矩陣的主對角矩陣Ncenternegative definite quaratic form negative semidefinite quadratic form nonhomogeneous equations nonsigular matrix nontrivial

52、 solution norm of vector V normalizing vector VOorthogonal basisorthogonal complementorthogonal decompositionorthogonally diagonalizable matrix orthogonal matrix orthogonal set orthonormal basisorthonomal setbPpartitioned matrixpositive definite matrixpositive definite quatratic form positive semide

53、finite matrix positive semidefinite quadratic form負(fù)定二次型半負(fù)定二次型非齊次線性方程組非奇異矩陣非平凡解向量V的范數(shù)規(guī)范化向量正交基正交補(bǔ)正交分解矩陣的正交對角化正交矩陣正交向量組規(guī)范正交基規(guī)范正交向量組分塊矩陣 正定矩陣 正定二次型 半正定矩陣 半正定二次型Qquatratic formcenterR/center rank of matrix A reduced echelon matrix row vector二次型矩陣A的秩r(A)最簡梯形陣行向量set spanned by similar matrices similarity t

54、ransformation singular matrix solution set standard basis standard matrix submatrix subspace symmetric matrix由向量 所生成相似矩陣相似變換奇異矩陣解集合標(biāo)準(zhǔn)基標(biāo)準(zhǔn)矢邱車I子矩陣子空間對稱矩陣AT矩陣A的跡tr(A)矩陣A的轉(zhuǎn)秩 三角不等式 平凡解trace of matrix A transpose of A triangle inequlity trivial solutionUunit vector單位向量upper triangular matrix上三角形矩陣Vvandermonde matrix范得蒙矩陣vector向量vector space向量空間零子空間零空間 (本文已被瀏覽 133次)Zzero subspacez