最新整理数学英文词汇大全知识讲解

1、此文档收集于网络，如有侵权，请联系网站删除微积分第一章函数与极限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补集complement set直积direct product笛卡儿积Cartesian product开区间open interval闭区间closed interval半开区间half open interval有限区间finite interval区间的长度length of an interval无限

2、区间infinite interval领域neighborhood领域的中心centre of a neighborhood领域的半径radius of a neighborhood左领域left neighborhood右领域right neighborhood映射mappingX 到 Y 的映射mapping of X ontoY满射surjection单射injection一一映射one-to-one mapping双射bijection算子operator变化transformation函数function逆映射inverse mapping复合映射composite mapping自

3、变量independent variable因变量dependent variable定义域domain函数值value of function函数关系function relation值域range自然定义域natural domain精品文档此文档收集于网络，如有侵权，请联系网站删除单值函数single valued function多值函数multiple valued function单值分支one-valued branch函数图形graph of a function绝对值函数absolute value符号函数sigh function整数部分integral part阶梯曲线s

4、tep curve当且仅当if and only if(iff)分段函数piecewise function上界upper bound下界lower bound有界boundedness无界unbounded函数的单调性monotonicity of a function单调增加的increasing单调减少的decreasing单调函数monotone function函数的奇偶性parity(odevity) of a function对称symmetry偶函数even function奇函数odd function函数的周期性periodicity of a function周期peri

5、od反函数inverse function直接函数direct function复合函数composite function中间变量intermediate variable函数的运算operation of function基本初等函数basic elementary function初等函数elementary function幂函数power function指数函数exponential function对数函数logarithmic function三角函数trigonometric function反三角函数inverse trigonometric function常数函数con

6、stant function双曲函数hyperbolic function双曲正弦hyperbolic sine双曲余弦hyperbolic cosine双曲正切hyperbolic tangent反双曲正弦inverse hyperbolic sine反双曲余弦inverse hyperbolic cosine反双曲正切inverse hyperbolic tangent精品文档此文档收集于网络，如有侵权，请联系网站删除极限limit数列sequence of number收敛convergence收敛于a converge to a发散divergent极限的唯一性uniqueness o

7、f limits收敛数列的有界性 boundedness of a convergent sequence 子列 subsequence函数的极限limits of functions函数当 x 趋于 x0 时的极限limit of functions as x approaches x0左极限left limit右极限right limit单侧极限one-sided limits水平渐近线horizontal asymptote无穷小infinitesimal无穷大infinity铅直渐近线vertical asymptote夹逼准则squeeze rule单调数列monotonic seq

8、uence高阶无穷小infinitesimal of higher order低阶无穷小infinitesimal of lower order同阶无穷小infinitesimal of the same order-2 高等数学 -翻译等阶无穷小equivalent infinitesimal函数的连续性continuity of a function增量increment函数在 x0 连续the function is continuous at x0左连续left continuous右连续right continuous区间上的连续函数continuous function函数 在该区

9、间上连续 function is continuous on an interval 不连续点 discontinuity point第一类间断点discontinuity point of the first kind第二类间断点discontinuity point of the second kind初等函数的连续性continuity of the elementary functions定义区间defined interval最大值global maximum value (absolute maximum)最小值global minimum value (absolute mini

10、mum)零点定理the zero point theorem介值定理intermediate value theorem精品文档此文档收集于网络，如有侵权，请联系网站删除第二章导数与微分Chapter2 Derivative and Differential速度velocity匀速运动uniform motion平均速度average velocity瞬时速度instantaneous velocity圆的切线tangent line of a circle切线tangent line切线的斜率slope of the tangent line位置函数position function导数de

11、rivative可导derivable函数的变化率问题 problem of the change rate of a function 导函数 derived function左导数left-hand derivative右导数right-hand derivative单侧导数one-sided derivatives在闭区间【 a,b】上可导is derivable on the closed interval a,b切线方程tangent equation角速度angular velocity成本函数cost function边际成本marginal cost链式法则chain rule

12、隐函数implicit function显函数explicit function二阶函数second derivative三阶导数third derivative高阶导数nth derivative莱布尼茨公式Leibniz formula对数求导法log- derivative参数方程parametric equation相关变化率correlative change rata微分differential可微的differentiable函数的微分differential of function自变量的微分differential of independent variable微商diffe

13、rential quotient间接测量误差indirect measurement error绝对误差absolute error相对误差relative error第三章微分中值定理与导数的应用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 罗马定理 Rolle s theorem精品文档此文档收集于网络，如有侵权，请联系网站删除费马引理Fermat s lemma拉格朗日中值定理Lagrange s mean value theorem驻点stationary point稳定点s

14、table point临界点critical point辅助函数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洛必达法则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余项remainder term拉格朗日余项Lagrange remainder term麦克劳

15、林公式Maclaurin s formula佩亚诺公式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 拐点 inflection point函数的极值extremum of function极大值local(relative) maximum最大值global(absolute) mximum极小值local(relative) minimum最小值global(absolute) minimum目标函数objective function

16、曲率curvature弧微分arc differential平均曲率average curvature曲率园circle of curvature曲率中心center of curvature曲率半径radius of curvature渐屈线evolute渐伸线involute根的隔离isolation of root隔离区间isolation interval切线法tangent line method第四章不定积分Chapter4 Indefinite Integrals原函数primitive function(antiderivative)积分号sign of integration

17、被积函数integrand精品文档此文档收集于网络，如有侵权，请联系网站删除积分变量integral variable积分曲线integral curve积分表table of integrals换元积分法integration by substitution分部积分法integration by parts分部积分公式formula of integration by parts有理函数rational function真分式proper fraction假分式improper fraction第五章定积分Chapter5 Definite Integrals曲边梯形trapezoid wi

18、th曲边curve edge窄矩形narrow rectangle曲边梯形的面积area of trapezoid with curved edge积分下限lower limit of integral积分上限upper limit of integral积分区间integral interval分割partition积分和integral sum可积integrable矩形法rectangle method积分中值定理mean value theorem of integrals函数在区间上的平均值 average value of a function on an integvals 牛顿

19、莱布尼茨公式 Newton-Leibniz formula微积分基本公式fundamental formula of calculus换元公式formula for integration by substitution递推公式recurrence formula反常积分improper integral反常积分发散the improper integral is divergent反常积分收敛the improper integral is convergent无穷限的反常积分improper integral on an infinite interval无界函数的反常积分 imprope

20、r integral of unbounded functions 绝对收敛 absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals元素法the element method面积元素element of area平面图形的面积area of a luane figure直角坐标又称“笛卡儿坐标(Cartesian coordinates)”极坐标polar coordinates抛物线parabola精品文档此文档收集于网络，如有侵权，请联系网站删除椭圆ellipse旋转体的面积volume o

21、f a solid of rotation旋转椭球体ellipsoid of revolution, ellipsoid of rotation曲线的弧长arc length of acurve可求长的rectifiable光滑smooth功 work水压力water pressure引力gravitation变力variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量vector自由向量free vector单位向量unit vector零向量zero vector相等equal平行pa

22、rallel向量的线性运算linear poeration of vector三角法则triangle rule平行四边形法则parallelogram rule交换律commutative law结合律associative law负向量negative vector差 difference分配律distributive law空间直角坐标系space rectangular coordinates坐标面coordinate plane卦限octant向量的模modulus of vector向量 a 与 b 的夹角angle between vector a and b方向余弦direct

23、ion cosine方向角direction angle向量在轴上的投影projection of a vector onto an axis数量积，外积，叉积 scalar product,dot product,inner product 曲面方程 equation for a surface 球面 sphere旋转曲面surface of revolution母线generating line轴 axis圆锥面cone顶点vertex旋转单叶双曲面revolution hyperboloids of one sheet精品文档此文档收集于网络，如有侵权，请联系网站删除旋转双叶双曲面rev

24、olution hyperboloids of two sheets柱面cylindrical surface ,cylinder圆柱面cylindrical surface准线directrix抛物柱面parabolic cylinder二次曲面quadric surface椭圆锥面dlliptic cone椭球面ellipsoid单叶双曲面hyperboloid of one sheet双叶双曲面hyperboloid of two sheets旋转椭球面ellipsoid of revolution椭圆抛物面elliptic paraboloid旋转抛物面paraboloid of re

25、volution双曲抛物面hyperbolic paraboloid马鞍面saddle surface椭圆柱面elliptic cylinder双曲柱面hyperbolic cylinder抛物柱面parabolic cylinder空间曲线space curve空间曲线的一般方程general form equations of a space curve空间曲线的参数方程parametric equations of a space curve螺转线spiral螺矩pitch投影柱面projecting cylinder投影projection平面的点法式方程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两平面的夹角angle between two planes点到平面的距离distance from a point to a plane空间直线的一般方程general equation of a line in space方向向量direction vector直线的点向式方程pointdirection form equations of a line方向数direction number直线的参数方程parametric equations

27、 of a line两直线的夹角angle between two lines垂直perpendicular直线与平面的夹角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系数行列式coefficient determinant精品文档此文档收集于网络，如有侵权，请联系网站删除第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Ap

28、plication 一元函数 function of one variable多元函数function of several variables内点interior point外点exterior point边界点frontier point,boundary point聚点point of accumulation开集openset闭集closed set连通集connected set开区域open region闭区域closed region有界集bounded set无界集unbounded setn 维空间n-dimentional space二重极限double limit多元函数

29、的连续性continuity of function of seveal连续函数continuous function不连续点discontinuity point一致连续uniformly continuous偏导数partial derivative对自变量 x 的偏导数 partial derivative with respect to independent variable x 高阶偏导数 partial derivative of higher order二阶偏导数second order partial derivative混合偏导数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必要条件necessary condition充分条件sufficient condition叠加原理superpostition principle全导数total derivative中间变量intermediate variable隐函数存在定理 theorem of the existence of implicit function 曲线的切向量 tangent vector of

31、a curve 法平面 normal plane向量方程vector equation向量值函数vector-valued function切平面tangent plane法线normal line方向导数directional derivative精品文档此文档收集于网络，如有侵权，请联系网站删除梯度gradient数量场scalar field梯度场gradient field向量场vector field势场potential field引力场gravitational field引力势gravitational potential曲面在一点的切平面tangent plane to a

32、surface at a point曲线在一点的法线normal line to a surface at a point无条件极值unconditional extreme values条件极值conditional extreme values拉格朗日乘数法Lagrange multiplier method拉格朗日乘子Lagrange multiplier经验公式empirical formula最小二乘法method of least squares均方误差mean square error第九章重积分Chapter9 Multiple Integrals二重积分double inte

33、gral可加性additivity累次积分iterated integral体积元素volume element三重积分triple integral直角坐标系中的体积元素 volume element in rectangular coordinate system 柱面坐标 cylindrical coordinates柱面坐标系中的体积元素 volume element in cylindrical coordinate system 球面坐标 spherical coordinates球面坐标系中的体积元素 volume element in spherical coordinate

34、system 反常二重积分 improper double integral 曲面的面积 area of a surface质心centre of mass静矩static moment密度density形心centroid转动惯量moment of inertia参变量parametric variable第十章曲线积分与曲面积分Chapter10 Line(Curve)Integrals and Surface Integrals对弧长的曲线积分line integrals with respect to arc hength第一类曲线积分line integrals of the fir

35、st type对坐标的曲线积分line integrals with respect to x,y,and z第二类曲线积分line integrals of the second type精品文档此文档收集于网络，如有侵权，请联系网站删除有向曲线弧directed arc单连通区域simple connected region复连通区域complex connected region格林公式Green formula第一类曲面积分surface integrals of the first type对面的曲面积分surface integrals with respect to area有向

36、曲面directed surface对坐标的曲面积分 surface integrals with respect to coordinate elements 第二类曲面积分 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环流量circulation旋度rotation,curl第十一章无穷级数

37、Chapter11 Infinite Series一般项general term部分和partial sum余项remainder term等比级数geometric series几何级数geometric series公比common ratio调和级数harmonic series柯西收敛准则Cauchy convergence criteria, Cauchy criteria for convergence正项级数series of positive terms达朗贝尔判别法D Alembert test柯西判别法Cauchy test交错级数alternating series绝对收

38、敛absolutely convergent条件收敛conditionally convergent柯西乘积Cauchy product函数项级数series of functions发散点point of divergence收敛点point of convergence收敛域convergence domain和函数sum function幂级数power series幂级数的系数coeffcients of power series阿贝尔定理Abel Theorem精品文档此文档收集于网络，如有侵权，请联系网站删除收敛半径radius of convergence收敛区间interval

39、 of convergence泰勒级数Taylor series麦克劳林级数Maclaurin series二项展开式binomial expansion近似计算approximate calculation舍入误差round-off error,rounding error欧拉公式Euler s formula魏尔斯特拉丝判别法Weierstrass test三角级数trigonometric series振幅amplitude角频率angular frequency初相initial phase矩形波square wave谐波分析harmonic analysis直流分量direct co

40、mponent基波fundamental wave二次谐波second harmonic三角函数系trigonometric function system傅立叶系数Fourier coefficient傅立叶级数Forrier series周期延拓periodic prolongation正弦级数sine series余弦级数cosine series奇延拓odd prolongation偶延拓even prolongation傅立叶级数的复数形式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微分方程的阶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初始条件initial condition微分方程的特解 particular solution of a differential e

42、quation 初值问题 initial value problem微分方程的积分曲线 integral curve of a differential equation 可分离变量的微分方程 variable separable differential equation 隐式解 implicit solution隐式通解inplicit general solution衰变系数decay coefficient精品文档此文档收集于网络，如有侵权，请联系网站删除衰变decay齐次方程homogeneous equation一阶线性方程linear differential equation

43、of first order非齐次non-homogeneous齐次线性方程homogeneous linear equation非齐次线性方程non-homogeneous linear equation常数变易法method of variation of constant暂态电流transient stata current稳态电流steady state current伯努利方程Bernoulli equation全微分方程total differential equation积分因子integrating factor高阶微分方程differential equation of hi

44、gher order悬链线catenary高阶线性微分方程linera differential equation of higher order自由振动的微分方程differential equation of free vibration强迫振动的微分方程differential equation of forced oscillation串联电路的振荡方程 oscillation equation of series circuit 二阶线性微分方程 second order linera differential equation 线性相关 linearly dependence 线性

45、无关 linearly independce二阶常系数齐次线性微分方程 second order homogeneour linear differential equation with constant coefficient二阶变系数齐次线性微分方程second order homogeneous linear differentialequation withvariable coefficient特征方程characteristic equation无阻尼自由振动的微分方程 differential equation of free vibration with zero dampi

46、ng 固有频率 natural frequency简谐振动 simple harmonic oscillation,simple harmonic vibration 微分算子 differential operator待定系数法method of undetermined coefficient共振现象resonance phenomenon欧拉方程Euler equation幂级数解法power series solution数值解法numerial solution勒让德方程Legendre equation微分方程组system of differential equations常系数

47、线性微分方程组system of linera differential equations with constant coefficient线性代数A精品文档此文档收集于网络，如有侵权，请联系网站删除adjont(adjugate) of matrix AA 的伴随矩阵augmented matrixA 的增广矩阵Bblock diagonal matrix块对角矩阵block matrix块矩阵basic solution set基础解系CCauchy-Schwarz inequality柯西 -许瓦兹不等式characteristic equation特征方程characteristi

48、c polynomial特征多项式coffcient matrix系数矩阵cofactor代数余子式cofactor expansion代数余子式展开column vector列向量commuting matrices交换矩阵consistent linear system相容线性方程组Cramer s rule克莱姆法则Cross- product term交叉项DDeterminant行列式Diagonal entries对角元素Diagonal matrix对角矩阵Dimension of a vector space V向量空间 V 的维数Eechelon matrix梯形矩阵eigenspace特征空间eigenvalue特征值eigenvector特征向量eigenvector basis特征向量的基elementary matrix初等矩阵elementary row operations行初等变换精品文档此文档收集于网络，如有侵权，请