最新整理數(shù)學英文詞匯大全知識講解

1、此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除微積分第一章函數(shù)與極限Chapter1 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

2、區(qū)間infinite interval領域neighborhood領域的中心centre of a neighborhood領域的半徑radius of a neighborhood左領域left neighborhood右領域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inverse mapping復合映射composite mapping自

3、變量independent variable因變量dependent variable定義域domain函數(shù)值value of function函數(shù)關系function relation值域range自然定義域natural domain精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除單值函數(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 part階梯曲線s

4、tep curve當且僅當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)的周期性periodicity of a function周期peri

5、od反函數(shù)inverse function直接函數(shù)direct function復合函數(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 function三角函數(shù)trigonometric function反三角函數(shù)inverse trigonometric function常數(shù)函數(shù)con

6、stant 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精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除極限limit數(shù)列sequence of number收斂convergence收斂于a converge to a發(fā)散divergent極限的唯一性uniqueness o

7、f 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 x 趨于 x0 時的極限limit of functions as x approaches x0左極限left limit右極限r(nóng)ight limit單側極限one-sided limits水平漸近線horizontal asymptote無窮小infinitesimal無窮大infinity鉛直漸近線vertical asymptote夾逼準則squeeze rule單調(diào)數(shù)列monotonic seq

8、uence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-2 高等數(shù)學 -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 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)

9、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 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 mini

10、mum)零點定理the zero point theorem介值定理intermediate value theorem精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除第二章導數(shù)與微分Chapter2 Derivative and Differential速度velocity勻速運動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tangent line切線的斜率slope of the tangent line位置函數(shù)position function導數(shù)de

11、rivative可導derivable函數(shù)的變化率問題 problem of the change rate of a function 導函數(shù) derived function左導數(shù)left-hand derivative右導數(shù)right-hand derivative單側導數(shù)one-sided derivatives在閉區(qū)間【 a,b】上可導is derivable 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鏈式法則chain rule

12、隱函數(shù)implicit function顯函數(shù)explicit function二階函數(shù)second derivative三階導數(shù)third derivative高階導數(shù)nth derivative萊布尼茨公式Leibniz formula對數(shù)求導法log- derivative參數(shù)方程parametric equation相關變化率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diffe

13、rential 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數(shù)的應用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 羅馬定理 Rolle s theorem精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除費馬引理Fermat s lemma拉格朗日中值定理Lagrange s mean value theorem駐點stationary point穩(wěn)定點s

14、table 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 Rule0/0 型不定式indeterminate 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

15、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 point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目標函數(shù)objective function

16、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 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

17、被積函數(shù)integrand精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除積分變量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 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Chapter5 Definite Integrals曲邊梯形trapezoid wi

18、th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分割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

19、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 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 imprope

20、r integral of unbounded functions 絕對收斂 absolutely convergent第六章定積分的應用Chapter6 Applications of the Definite Integrals元素法the element method面積元素element of area平面圖形的面積area of a luane figure直角坐標又稱“笛卡兒坐標(Cartesian coordinates)”極坐標polar coordinates拋物線parabola精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除橢圓ellipse旋轉體的面積volume o

21、f a solid of rotation旋轉橢球體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引力gravitation變力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pa

22、rallel向量的線性運算linear poeration of vector三角法則triangle rule平行四邊形法則parallelogram rule交換律commutative law結合律associative law負向量negative vector差 difference分配律distributive law空間直角坐標系space rectangular coordinates坐標面coordinate plane卦限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direct

23、ion 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 for a surface 球面 sphere旋轉曲面surface of revolution母線generating line軸 axis圓錐面cone頂點vertex旋轉單葉雙曲面revolution hyperboloids of one sheet精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除旋轉雙葉雙曲面rev

24、olution hyperboloids of two sheets柱面cylindrical surface ,cylinder圓柱面cylindrical surface準線directrix拋物柱面parabolic cylinder二次曲面quadric 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旋轉橢球面ellipsoid of revolution橢圓拋物面elliptic paraboloid旋轉拋物面paraboloid of re

25、volution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螺轉線spiral螺矩pitch投影柱面projecting cylinder投影projection平面的點法式方程pointnorm form

26、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

27、 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 a pencil of planes行列式determinant系數(shù)行列式coefficient determinant精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除第八章多元函數(shù)微分法及其應用Chapter8 Differentiation of Functions of Several Variables and Its Ap

28、plication 一元函數(shù) function of one variable多元函數(shù)function of several variables內(nèi)點interior point外點exterior point邊界點frontier 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 setn 維空間n-dimentional space二重極限double limit多元函數(shù)

29、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)uniformly continuous偏導數(shù)partial derivative對自變量 x 的偏導數(shù) partial derivative with respect to independent variable x 高階偏導數(shù) partial derivative of higher order二階偏導數(shù)second order partial derivative混合偏導數(shù)hybrid partial derivat

30、ive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充分條件sufficient condition疊加原理superpostition principle全導數(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

31、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 derivative精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除梯度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引力勢gravitational potential曲面在一點的切平面tangent plane to a

32、surface at a point曲線在一點的法線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Chapter9 Multiple Integrals二重積分double inte

33、gral可加性additivity累次積分iterated integral體積元素volume element三重積分triple integral直角坐標系中的體積元素 volume element in rectangular coordinate system 柱面坐標 cylindrical coordinates柱面坐標系中的體積元素 volume element in cylindrical coordinate system 球面坐標 spherical coordinates球面坐標系中的體積元素 volume element in spherical coordinate

34、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轉動慣量moment of inertia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 fir

35、st type對坐標的曲線積分line integrals with respect to x,y,and z第二類曲線積分line integrals of the second type精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除有向曲線弧directed arc單連通區(qū)域simple connected region復連通區(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

36、曲面directed surface對坐標的曲面積分 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 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)

37、Chapter11 Infinite Series一般項general term部分和partial sum余項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 series柯西收斂準則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

38、斂absolutely convergent條件收斂conditionally 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精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除收斂半徑radius of convergence收斂區(qū)間interval

39、 of convergence泰勒級數(shù)Taylor series麥克勞林級數(shù)Maclaurin 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 co

40、mponent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 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)的復數(shù)形式complex form of Fourier series第十二章微分方程Chapter12 Differential Equation解微分方

41、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 e

42、quation 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 separable differential equation 隱式解 implicit solution隱式通解inplicit general solution衰變系數(shù)decay coefficient精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除衰變decay齊次方程homogeneous equation一階線性方程linear differential equation

43、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 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 hi

44、gher order懸鏈線catenary高階線性微分方程linera differential equation of higher order自由振動的微分方程differential equation of free vibration強迫振動的微分方程differential equation of forced oscillation串聯(lián)電路的振蕩方程 oscillation equation of series circuit 二階線性微分方程 second order linera differential equation 線性相關 linearly dependence 線性

45、無關 linearly independce二階常系數(shù)齊次線性微分方程 second order homogeneour linear differential equation with constant coefficient二階變系數(shù)齊次線性微分方程second order homogeneous linear differentialequation 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 dampi

46、ng 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 of undetermined coefficient共振現(xiàn)象resonance phenomenon歐拉方程Euler equation冪級數(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)

47、線性微分方程組system of linera differential equations with constant coefficient線性代數(shù)A精品文檔此文檔收集于網(wǎng)絡，如有侵權，請聯(lián)系網(wǎng)站刪除adjont(adjugate) of matrix AA 的伴隨矩陣augmented matrixA 的增廣矩陣Bblock diagonal matrix塊對角矩陣block matrix塊矩陣basic solution set基礎解系CCauchy-Schwarz inequality柯西 -許瓦茲不等式characteristic equation特征方程characteristi

48、c polynomial特征多項式coffcient matrix系數(shù)矩陣cofactor代數(shù)余子式cofactor expansion代數(shù)余子式展開column vector列向量commuting matrices交換矩陣consistent linear system相容線性方程組Cramer s rule克萊姆法則Cross- product term交叉項DDeterminant行列式Diagonal entries對角元素Diagonal matrix對角矩陣Dimension of a vector space V向量空間 V 的維數(shù)Eechelon matrix梯形矩陣eigenspace特征空間eigenvalue特征值eigenvector特征向量eigenvector basis特征向量的基elementary matrix初等矩陣elementary row operations行初等變換精品文檔此文檔收集于網(wǎng)絡，如有侵權，請