实变函数与泛函分析中的英文单词和短语

英汉微积分词汇English-Chinese Calculus Vocabulary第一章函数与极限Chapter 1 Function and Limit高等数学higher mathematics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象限quadrant原点origin坐标coordinate轴axisx 轴x-axis整数integer有理数rational number实数real number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无限区间infinite interval领域neighborhood领域的中心center 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 onto Y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absolute value绝对值函数absolute value function符号函数sigh function整数部分integral part阶梯曲线step 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最小上界least upper bound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严格递减strictly decreasing严格递增strictly increasing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period周期函数periodic function反函数inverse function直接函数direct function函数的复合composition of 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线性函数linear function常数函数constant function多项式polynomial分段定义函数piecewise defined function阶梯函数step function幂函数power function指数函数exponential function指数exponent自然指数函数natural exponential function对数logarithm对数函数logarithmic function自然对数函数natural logarithm function三角函数trigonometric function正弦函数sine function余弦函数cosine function正切函数tangent function半角公式half-angle formulas反三角函数inverse trigonometric function常数函数constant function双曲线hyperbola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最优化问题optimization problems不等式inequality极限limit数列sequence of number复利compound interest收敛convergence收敛的convergent收敛于a converge to a发散divergence发散的divergent极限的唯一性uniqueness of 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0x 时的极限 limit of functions as x approaches 0x单侧极限 one-sided limit左极限 left limit右极限 right limit单侧极限 one-sided limits渐近线 asymptote水平渐近线 horizontal asymptote分式 fractions商定律 quotient rule无穷小 infinitesimal无穷大 infinity铅直渐近线 vertical asymptote夹逼准则 squeeze rule (Sandwich theorem)单调数列 monotonic sequence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等阶无穷小 equivalent infinitesimal多项式的次数 degree of a polynomial三次函数 cubic function函数的连续性 continuity of a function增量 increment函数在0x 连续 the function is continuous at 0x左连续 left continuous / continuous from the left右连续 right continuous / continuous from the right连续性 continuity不连续性 discontinuity连续函数 continuous function函数在区间上连续 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 minimum)零点定理 the zero point theorem介值定理 intermediate value theorem第二章 导数与微分Chapter 2 Derivative and Differential 速度velocity速率speed平均速度average velocity瞬时速度instantaneous 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割线secant line切线tangent line位置函数position function导数derivative求导法differentiation可导的derivable可导函数differentiable function光滑曲线smooth curve变化率rate of change函数的变化率问题problem of the change rate of a function导函数derived function导数定义域domain of derivative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] 指数函数的导数derivative of exponential function幂函数的导数derivative of power function切线的斜率slope of the tangent line截距interceptsx 截距x-intercept直线的斜截式slope-intercept equation of a line点斜式point-slope form切线方程tangent equation焦点focus角速度angular velocity成本函数cost function边际成本marginal cost逐项求导法differentiation term by term积之导数derivative of a product商之导数derivative of a quotient链式法则chain rule隐函数implicit function显函数explicit function隐函数求导法implicit differentiation加速度acceleration二阶导数second derivative三阶导数third derivative高阶导数nth derivative / higher derivative莱布尼茨公式Leibniz formula对数求导法log- derivative参数parameter参数方程parametric equation相关变化率correlative change rata微分differential微分学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differential quotient逼近法approximation用微分逼近approximation by differentials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Chapter 3 MeanValue Theorems of Differentials and the Application ofDerivatives均值定理mean value theorem罗尔定理Roll’s theorem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stable 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 Rule不定式indeterminate form“0”型不定式indeterminate form of type “”泰勒中值定理Taylor’s mean value theorem 泰勒公式Taylor formula系数coefficient余项remainder term线性近似linear approximation拉格朗日余项Lagrange remainder term麦克劳林公式Maclaurin’s formula佩亚诺余项Peano remainder term阶乘factorial凹凸性concavity上凹（或下凸）concave upward (concave up)下凹（或向上凸的）concave downward (concave down) 拐点inflection point极值extreme value函数的极值extremum of function极大与极小值maximum and minimum values极大值local (relative) maximum最大值global (absolute) maximum极小值local (relative) minimum最小值global (absolute) minimum目标函数objective function收入函数revenue function斜渐进线slant asymptote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Chapter 4 Indefinite Integrals 原函数primitive function / antiderivative积分integration积分学integral积分号sign of integration被积函数integrand积分变量integral variable积分常数constant of integration积分曲线integral curve积分表table of integrals换元积分法integration by substitution有理代换法rationalizing substitution三角代换法trigonometric substitutions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部分分式partial fractions三角积分trigonometric integrals第五章定积分Chapter 5 Definite Integrals曲线下方之面积area under a curve曲边梯形trapezoid with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黎曼和Riemannian sum积分和integral sum可积的integrableSimpson 法则逼近法approximation by Simpson’s rule梯形法则逼近法approximation by trapezoidal rule矩形法rectangle method曲线之间的面积area between curves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 interval 牛顿－莱布尼茨公式Newton-Leibniz formula微积分基本公式fundamental formula of calculus微积分基本定理fundamental theorem of calculus变量代换change of variable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improper integral of unbounded functions瑕点flaw绝对收敛absolutely convergent第六章定积分的应用Chapter 6 Applications of the Definite Integrals 元素法the element method面积元素element of area平面plane平面图形的面积area of a plane figure直角坐标（又称“笛卡儿坐标”）Cartesian coordinates / rectangular coordinates x 坐标x-coordinate坐标轴coordinate axes极坐标polar coordinates极轴polar axis极点pole圆circle扇形sector抛物线parabola椭圆ellipse椭圆的轴axes of ellipse蚌线conchoid外摆线epicycloid双纽线lemniscate蚶线limacon旋转体solid of revolution, solid of rotation旋转体的面积volume of a solid of rotation旋转椭球体ellipsoid of revolution, ellipsoid of rotation曲线的弧长arc length of a curve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Chapter 7 Space Analytic Geometry and Vector Algebra纯量（标量）scalar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parallel平行线parallel lines向量的线性运算linear operation of vector加法addition减法subtraction数乘运算scalar multiplication三角形法则triangle rule平行四边形法则parallelogram rule交换律commutative law结合律associative law分配律distributive law负向量negative vector三角不等式triangle inequality对角线diagonal差difference余弦定理（定律）law of cosines空间space空间直角坐标系space rectangular coordinates坐标平面coordinate plane卦限octant向量的模modulus of vector定比分点definite proportion and separated point中点公式midpoint formula等腰三角形isosceles triangle向量a与b的夹角angle between vector a and b方向余弦direction cosine方向角direction angle投影projection向量在轴上的投影projection of a vector onto an axis向量的分量components of a vector对称点symmetric point数量积（点积，内积）scalar product (dot product, inner product)叉积（向量积，外积）cross product (vector product, exterior product) 混合积mixed product锐角acute angle流体fluid刚体rigid body角速度angular velocity平行六面体parallelepiped平面的点法式方程point-norm form equation of a plane法向量normal vector平面的一般方程general form equation of a plane三元一次方程three-variable linear equation平面的截距式方程intercept 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point-direction form equations of a line直线的对称式方程symmetric form equation of a line方向数direction number直线的参数方程parametric equations of a line两直线的夹角angle between two lines垂直perpendicular垂直线perpendicular lines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曲面方程equation for a surface球面sphere球体spheroid球心ball center轨迹方程locus equation旋转轴rotation axis旋转曲面surface of revolution母线generating line圆锥面cone顶点vertex半顶角semi-vertical angle旋转双曲面revolution hyperboloids旋转单叶双曲面revolution hyperboloids of one sheet 旋转双叶双曲面revolution hyperboloids of two sheets 柱面cylindrical surface, cylinder圆柱circular cylinder圆柱面cylindrical surface准线directrix抛物柱面parabolic cylinder二次曲面quadric surface截痕法method of cut-off mark椭圆锥面elliptic cone椭球面ellipsoid双曲面hyperboloid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抛物面paraboloid椭圆体ellipsoid椭圆抛物面elliptic paraboloid旋转抛物面paraboloid of revolution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交线intersection 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螺线spiral / helix螺矩pitch投影柱面projecting cylinder第八章多元函数微分法及其应用Chapter 8 Differentiation of Functions of Several Variables and Its Application 一元函数function of one variable二元函数binary function邻域neighborhood去心邻域noncentral neighborhood方邻域square neighborhood圆邻域circular neighborhood内点interior point外点exterior point边界点frontier point, boundary point聚点point of accumulation导集derived set开集open set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-dimensional space多元函数function of several variables二重极限double limit多元函数的连续性continuity of function of several variables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 derivative全微分total differential偏增量partial 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superposition 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 光滑曲面smooth surface曲线的切向量tangent vector of 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等高线level curve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 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鞍点saddle point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Chapter 9 Multiple Integrals重积分multiple integrals二重积分double integral可加性additivity累次（逐次）积分iterated integral体积元素volume element二重积分变量代换法change of variable in double integral极坐标表示的面积area in polar coordinates扇形的面积area of a sector of a circle极坐标二重积分double integral in polar coordinates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 system 剥壳法shell method圆盘法disk method反常二重积分improper double integral曲面的面积area of a surface质心center 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Chapter 10 Line (Curve) Integrals and Surface Integrals对弧长的曲线积分line integrals with respect to arc length第一类曲线积分line integrals of the first 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有向曲线弧directed arc单连通区域simple connected region复连通区域complex connected region路径无关path independence格林公式Green formula顺时针方向clockwise逆时针方向counterclockwise区域边界的正向positive direction of region boundary第一类曲面积分surface integrals of the first type旋转曲面的面积area of a surface of a revolution对面积的曲面积分surface integrals with respect to area有向曲面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有向曲面之元素element of directed surface高斯公式gauss formula拉普拉斯算子Laplace operator拉普拉斯变换Laplace transform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Chapter 11 Infinite Series一般项general term部分和partial sum收敛级数convergent series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coefficients of power series阿贝尔定理Abel Theorem收敛半径radius of convergence收敛区间interval of convergence幂级数的导数derivative of power series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魏尔斯特拉斯判别法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 component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Fourier 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Chapter 12 Differential Equation解微分方程solve a differential equation常微分方程ordinary differential equation (ODE)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 equation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implicit general solution衰变系数decay coefficient衰变decay齐次方程homogeneous equation一阶线性方程linear differential equation 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 state 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 higher order悬链线catenary高阶线性微分方程linear 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 linear differential equation线性相关linearly dependence线性无关linearly independence二阶常系数齐次线性微分方程second order homogeneous linear differential equation with constant coefficient二阶变系数齐次线性微分方程second order homogeneous linear differential equation with variable 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 damping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numerical solution勒让德方程Legendre equation微分方程组system of differential equations常系数线性微分方程组system of linear differential equations with constant coefficient。

《实变函数与泛函分析》课程教学大纲一、课程基本信息课程代码：110047课程名称：实变函数与泛函分析英文名称：Real variable analysis And Functional analysis课程类别：专业基础课学时：50学分：3适用对象：信息与计算科学专业本科考核方式：考试，平时成绩30％，期末成绩70％先修课程：数学分析和高等代数二、课程简介中文简介：实变函数起源于对连续而不可微函数以及Riemann可积函数等的透彻研究，在点集论的基础上讨论分析数学中一些最基本的概念和性质，其主要内容是引入Lebesgue积分并克服了Riemann积分的不足。

它是数学分析的继续、深化和推广，是一门培养学生数学素质的重要课程，也是现代数学的基础。

泛函分析起源于经典的数学物理边值问题和变分问题，同时概括了经典分析的许多重要概念，是现代数学中一个重要的分支，它综合运用了分析、代数与几何的观点和方法研究、分析数学和工程问题，其理论与方法具有高度概括性和广泛应用性的特点。

英文简介：Real variable analysis And Functional analysis is a theoreticalcourse of mathematics which can be used in variable fields such as engineeringand technology, physics, chemical, biology, economic and other fields. Theeducational aim in this course is to develop the abilities of students inanalyzing and solving practical problem by the special ways of Real variableanalysis And Functional analysis' thinking and reasoning.三、课程性质与教学目的本课程是在实变函数与泛函分析基本理论的基础上，着重泛函分析的应用，教学的目的是丰富学生的知识和培养学生解决实际问题的能力。

数学专业英语词汇（F）f distribution f分布f ratio 方差比f space f空间f test f检定face 面face centered 面心的face centered cubic 面心立方体的face of a polyhedron 多面体面face operator 面算子factor 因子factor analysis 因子分析factor combination 因子组合factor group 商群factor groupoid 商广群factor loading 因子载荷factor matrix 因子矩阵factor model 因子模型factor module 商模factor of a polynomial 多项式的因子factor of proportionality 比例系数factor out 提出撰因子factor ring 商环factor set 商集factor space 商空间factor system 因子组factor theorem 因子定理factorability 因子可分解性factorable 可因子分解的factorial 阶乘factorial cumulant 阶乘累积量factorial design 因子设计factorial experiment 析因实验factorial notation 阶乘记号factorial of an integer 整数的阶乘factorial polynomial 阶乘多项式factorial series 阶乘级数thermocouple pyrometer 热电偶高温计factoring 因式分解factorizable 可因子分解的factorization 因式分解factorization method 因子分解方法factorization theorem 因子分解定理factorize 因子分解fair game 适当对策faithful anti representation 一一反表示faithful functor 一一的函子faithful module 一一的模faithful representation 一一表示faithfully flat ring 一一平坦环false 假的false conclusion 假结论family 族family of curves 曲线族family of elements 元素族family of functions 函数族family of orthogonal curves 正交曲线族family of planes 平面族family of sets 集族family of solutions 解族family of surfaces 曲面族fan 扇形farey series 法雷级数fast fourier transformation 快速傅里叶变换fatou lemma 法都引理favorable case 有利情形favorable event 有利事件feasible base 可行基feasible constraint 可行约束feasible control 可行控制feasible direction 可行方向feasible point 可行点feasible region 可行区域feasible restriction 可行约束feasible solution 可行解feeble solution 弱解fermat last theorem 费马最后定理fermat number 费马数fermat spiral 费马螺线fermat theorem 费马定理feynman integral 费曼积分fiber 纤维fiber bundle 纤维丛fiber map 纤维映射fiber preserving mapping 保纤映射fiber space 纤维空间fibonacci number 斐波那契数fibring 纤维空间fiducial distribution 置信分布fiducial estimation 置信估计fiducial inference 置信推理fiducial limit 置信限fiducial probability 置信概率fiducial region 置信区域field 域;场field of algebraic functions 代数函数域field of constants 常数域field of definition 定义域field of events 事件场field of extremals 极值曲线场field of forces 力场field of numbers 数域field of rational functions 有理函数域field of rationals 有理数域field of real numbers 实数域field of scalars 系数域field of sets 集域field theory 域论;场论figure 图形filter 滤子filter base 滤子基filtered category 滤子化范畴filtered degree 滤子化次数filtered group 过滤群filtering 过滤filtration 过滤final decision 最后判决final functor 尾函子final state 终态final topology 终拓扑fine sheaf 强层fine topology 细拓扑fineness 细度finer topology 较细拓扑finish time 终止时间finite automaton 有限自动机finite base 有限基finite cardinal 有限基数finite constructibility 有限可构成性finite continued fraction 有限连分数finite cyclic group 有限循环群finite definability 有限可定义性finite difference approximation 有限差分逼近finite difference equation 有限差分方程finite dimensional 有限维的finite dimensional extension field 有限维扩张域finite dimensional operator 有限维算子finite discontinuity 有限不连续性finite element method 有限元法finite equation 有限方程finite extension 有限维扩张域finite field 有限域finite function 有限函数finite game 有限对策finite group 有限群finite induction 有限归纳法finite mathematics 有限数学finite measure 有限测度finite model 有限模型finite multiplier 有限乘数finite nilpotent group 有限幂零群finite number plane 有限数平面finite ordinal number 有限序数finite part 有限部分finite partition 有限划分finite point 有限点finite presentation 有限表示finite progression 有限级数finite quantity 有限量finite sequence 有限序列finite series 有限级数finite set 有限集finite sum 有限和finite valued function 有限值函数finitely additive 有限加性的finitely additive measure 有限加性测度finitely cocomplete category 有限共完全范畴finitely complete category 有限完全范畴finitely generatable vector space 有限可生成向量空间finitely generated abelian group 有限生成阿贝耳群finitely generated algebra 有限生成代数finitely generated extension field 有限生成扩张域finitely generated group 有限生成群finitely generated ideal 有限生成理想finitely generated module 有限生成模finitely presented 有限出现的finitely presented group 有限出现群finitely representable 有限可表示的finitely valued function 有限值函数finiteness 有限性finiteness principle 有限性原理finiteness theorem 有限性原理finsler manifold 芬斯莱廖first approximation 首次近似first axiom of countability 第一可数性公理first boundary condition 狄利克雷边界条件first boundary value problem 狄利克雷问题first class 第一类first comparison test 第一比较检验first derivative 一阶导数first fundamental form 第一基本形式first fundamental form of surface 曲面的第一基本形式first integral 初积分first isomorphism theorem 同态定理first mean value theorem 平均值定理first obstruction 第一障碍类first order theory 一阶理论first quadrant 第一象限first quartile 第一四分位数first term 首项first theorem of the mean 第一平均值定理fisher z distribution 费歇耳z分布fitted curve 拟合曲线fitting 拟合five color theorem 五色定理five figure 五位数的five point finite difference scheme 五点有限差分格式five sided 五面的fix 固定fixed element 不变元fixed error 偏倚fixed point 定点fixed point calculation 定点计算fixed point method 不动点法fixed point of mapping 映射的不动点fixed point representation 定点表示法fixed point theorem 不动点定理fixed sample 固定样本fixed vector 固定向量flabby resolution 松弛分解flabby sheaf 散射层flag 旗flag manifold 旗廖flat morphism 平坦射flat point 平坦点flat space 平坦空间flat surface 平面flatness 平坦性flecnode 拐结点flex 拐点floating point 浮点floating point calculation 浮点记数法floating point notation 浮点记数法floating point representation 浮点记数法flow 流flow line 吝flow of scalar field 纯量场的流flow problem 潦题fluctuation 起状fluent 变数fluid 铃fluid dynamics 铃动力学fluid mechanics 铃力学flux 量flux of the vector 量fluxion 导数focal axis 焦轴focal chord 焦弦focal circle 焦圆focal conic 焦点圆锥曲线focal distance 焦距focal length 焦距focal line 焦线focal plane 焦平面focal point 焦点focal radius 焦半径focal strip 焦带focal surface 焦曲面focus 焦点focus of a parabola 抛物线的焦点fold singularity 折奇性folding 卷积foliated manifold 叶状廖foliation 叶状结构folium 叶形线folium of descartes 笛卡儿叶形线follow 跟foot 垂足foot of a perpendicular 垂足force 力force function 力函数force of gravity 重力force of inertia 惯性力force polygon 力的多角形force triangle 力三角形force vector 力向量forced oscillation 受迫振动forced vibration 受迫振动forcing method 力迫法forecasting 预报form 形式formal 形式的formal derivative 形式导数formal language 形式语言formal logic 形式逻辑formal model 形式模型formal power series 形式幂级数formal system 形式系统formally real field 形式实域formation 形成formation rule 形成规则formless 无形状的formula 公式formula language 公式语言formula of computation 计算公式formula of propositional logic 命题逻辑公式formulate 公式化formulation 用公式表示forward difference 前向差分forward difference operator 前向差分算子forward difference quotient 前向差商forward solution 前向解法foundation 基础foundation of geometry 几何基础foundations of geometry 几何基础foundations of mathematics 数学基础four address 四地址的four address instruction 四地址指令four color conjecture 四色猜想four color problem 四色问题four color theorem 四色定理four digit 四位的four dimensional 四维的four dimensionality 四维性four fold table 四重表four vector 四元向量four vertex theorem 四顶点定理fourier analysis 傅里叶分析fourier analyzer 傅里叶分析仪fourier bessel series 傅里叶贝塞耳级数fourier bessel transformation 汉克尔变换fourier coefficient 傅里叶系数fourier cosine transform 傅里叶余弦变换fourier expansion 傅里叶展开fourier integral 傅里叶积分fourier integral equation 傅里叶积分方程fourier integral theorem 傅里叶积分定理fourier kernel 傅里叶核fourier series 傅里叶级数fourier sine transform 傅里叶正弦变换fourier synthesis 傅里叶综合法fourier transform 傅里叶变换fourierstieltjes transform 傅里叶斯蒂尔吉斯变换fractal 分形fractal dimension 分形维数fraction 分数fraction in lowest terms 最简分数fractional derivative 分数导数fractional equation 分数方程fractional exponent 分式指数fractional function 分数函数fractional ideal 分式理想fractional integral 分数次积分fractional number 分数fractional part 分数部分fractional rational function 分数有理函数fractional replication 分数配置fractionary ideal 分式理想frame 架frechet derivative 弗雷谢导数frechet differentiable function 弗莱谢可微函数frechet differential 弗雷谢微分frechet space f空间fredholm alternative 弗雷德霍姆择一fredholm alternative theorem 弗雷德霍姆择一定理fredholm determinant 弗雷德霍姆行列式fredholm integral equation 弗雷德霍姆积分方程fredholm operator 弗雷德霍姆算子fredholm point 弗雷德霍姆点fredholm radius 弗雷德霍姆半径fredholm type integral equation 弗雷德霍姆型积分方程free decision variable 自由决策变量free end 自由端free group 自由群free groupoid 自由广群free index 自由指标free liberty 自由可动性free mobility 自由可动性free monoid 自由独异点free optimization problem 自由最优化问题free product 自由积free semigroup 自由半群free subscript 自由添标free ultrafilter 自由超滤子free variable 自由变量free vector 自由向量frequency 频率frequency curve 频率曲线frequency diagram 频率图frequency distribution 频率分布frequency function 频率函数frequency polygon 频数多边形frequency theory of probability 概率的频率论fresnel integral 菲涅耳积分friction 摩擦frobenius algebra 弗罗宾尼斯代数frobenius automorphism 弗罗宾尼斯自同构frobenius group 弗罗宾尼斯群front 前面frontier 边界frontier point 边界点frustum of a paraboloid 平截头抛物面体frustum of cone 平截头圆锥体frustum of pyramid 截棱锥fubini theorem 富比尼定理fuchsian function 富克斯函数fuchsian group 富克斯群fulcrum 支点full inhomogeneous lorentz group 完全非齐次洛伦茨群full line 实线full linear group 全线性群full solid angle 完全立体角full subcategory 完全子范畴full unimodular group 完全幺模群fully faithful 完全一一的fully faithful functor 完全一一函子fully normal space 仿紧空间fully reducible star body 完全可约星形体fully transitive group 全可迁群function 函数function algebra 函数代数function chart 函数尺function code 操纂function constant 函数常数function continuous on the right 右连续函数function field 函数域function of bounded variation 有界变差函数function of class 类函数function of complex variable 复变函数function of confluent type 合镣函数function of function 合成函数function of n variables n元函数function of one variable 一元函数function of several real variables 多实元函数function of several variables 多元函数function of third order 三阶函数function of unbounded variation 无界变差函数function representation 函数表示function sequence 函数序列function series 函数级数function space 函数空间function symbol of n arguments n变数函数符号function theoretic 函数论的function theoretic null set 函数论的零集function theory 函数论function value 函数值function variable 函数变数functional 泛函functional analysis 泛函分析functional calculus 函项演算functional constant 函数常数functional dependence 函数相关functional determinant 函数行列式functional differential equation 泛函微分方程functional equation 函数方程functional expression 函数式functional matrix 函数矩阵functional relation 函数关系functional scale 函数尺functional space 函数空间functional symbol 函数符号functional transformation 泛函变换functionelement 函数元素functor 函子fundamental 基本的fundamental class 基本类fundamental cocycle 基本上循环fundamental conjunction 基本合取fundamental constants 基本常数fundamental curve 基本曲线fundamental cycle 基本闭链fundamental determinant 基本行列式fundamental discriminant 基本判别式fundamental domain 基本域fundamental element 基本元素thermocouple pyrometer 热电偶高温计fundamental equations 基本方程fundamental form 基本形式fundamental formulae 基本公式fundamental frequency 基频fundamental function 特寨数fundamental group 基本群fundamental groupoid 基本广群fundamental homology class 基本同掂fundamental identity 基本恒等式fundamental invariant 基本不变量fundamental law 基本律fundamental lemma 基本引理fundamental lemma of calculus of variation 变分法的基本引理fundamental matrix 基本矩阵fundamental net 基本有向点族fundamental parallelepipedon 基本平行六面体fundamental period 基本周期fundamental period parallellogram 基本周期平行四边形fundamental period parallelogram 原始周期平行四边形fundamental point 基本点fundamental polygon 基本多角形fundamental sequence 柯悟列fundamental set 基本集fundamental solution 基本解fundamental surface 基本曲面fundamental system of solutions 基本解组fundamental tensor 基本张量fundamental tetrahedron 基本四面体fundamental theorem 基本定理fundamental theorem of algebra 代数基本定理fundamental theorem of calculus 微积分基本定理fundamental transformation 基本变换fundamental unit 基本单位fundamentals 原理fuzzy set 模糊集。

《实变函数与泛函分析》课程教学大纲一、课程基本信息课程代码：110047课程名称：实变函数与泛函分析英文名称：Real variable analysis And Functional analysis课程类别：专业基础课学时：50学分：3适用对象：信息与计算科学专业本科考核方式：考试，平时成绩30％，期末成绩70％先修课程：数学分析和高等代数二、课程简介中文简介：实变函数起源于对连续而不可微函数以及Riemann可积函数等的透彻研究，在点集论的基础上讨论分析数学中一些最基本的概念和性质，其主要内容是引入Lebesgue积分并克服了Riemann积分的不足。

它是数学分析的继续、深化和推广，是一门培养学生数学素质的重要课程，也是现代数学的基础。

泛函分析起源于经典的数学物理边值问题和变分问题，同时概括了经典分析的许多重要概念，是现代数学中一个重要的分支，它综合运用了分析、代数与几何的观点和方法研究、分析数学和工程问题，其理论与方法具有高度概括性和广泛应用性的特点。

英文简介：Real variable analysis And Functional analysis is a theoretical course of mathematics which can be used in variable fields such as engineering and technology, physics, chemical, biology, economic and other fields. The educational aim in this course is to develop the abilities of students in analyzing and solving practical problem by the special ways of Real variable analysis And Functional analysis’ thinking and reasoning.三、课程性质与教学目的本课程是在实变函数与泛函分析基本理论的基础上，着重泛函分析的应用，教学的目的是丰富学生的知识和培养学生解决实际问题的能力。

V alue of function ：函数值V ariable ：变数V ector ：向量V elocity ：速度V ertical asymptote ：垂直渐近线V olume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean V alue Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected V alued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme V alue Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differentia l equation ：微分方程partial ：偏微分方程Differentia tion ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分C:Calculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean V alue Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、B:Absolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。

高等数学英语词汇高等数学英语词汇引导语：高等数学指相对于初等数学而言，数学的对象及方法较为繁杂的'一部分。

以下是店铺分享给大家的高等数学英语词汇，欢迎阅读!Aabelian group：阿贝尔群; absolute geometry：绝对几何; absolute value：绝对值; abstract algebra：抽象代数; addition：加法; algebra：代数; algebraicclosure：代数闭包; algebraic geometry：代数几何;algebraic geometry and analytic geometry：代数几何和解析几何; algebraic numbers：代数数; algorithm：算法; almost all：绝大多数; analytic function：解析函数; analytic geometry：解析几何; and：且;angle：角度; anticommutative：反交换律; antisymmetric relation：反对称关系; antisymmetry：反对称性; approximately equal：约等于; Archimedean field：阿基米德域; Archimedean group：阿基米德群; area：面积; arithmetic：算术; associative algebra：结合代数; associativity：结合律; axiom：公理; axiom of constructibility：可构造公理; axiom of empty set：空集公理;axiom of extensionality：外延公理; axiom of foundation：正则公理; axiom of pairing：对集公理; axiom of regularity：正则公理; axiom of replacement：代换公理; axiom of union：并集公理; axiom schema of separation：分离公理; axiom schema of specification：分离公理;axiomatic set theory：公理集合论; axiomatic system：公理系统;BBaire space：贝利空间; basis：基; Bézout's identity：贝祖恒等式; Bernoulli's inequality：伯努利不等式 ; Big O notation：大O符号; bilinear operator：双线性算子; binary operation：二元运算; binary predicate：二元谓词; binary relation：二元关系; Booleanalgebra：布尔代数;Boolean logic：布尔逻辑; Boolean ring：布尔环; boundary：边界; boundary point：边界点;bounded lattice：有界格;Ccalculus：微积分学; Cantor's diagonal argument：康托尔对角线方法; cardinal number：基数;cardinality：势; cardinality of the continuum：连续统的势; Cartesian coordinate system：直角坐标系; Cartesian product：笛卡尔积; category：范畴; Cauchy sequence：柯西序列; Cauchy-Schwarz inequality：柯西不等式; Ceva's Theorem：塞瓦定理; characteristic：特征;characteristic polynomial：特征多项式; circle：圆; class：类; closed：闭集; closure：封闭性或闭包; closure algebra：闭包代数; combinatorial identities：组合恒等式; commutativegroup：交换群; commutative ring：交换环; commutativity:：交换律; compact：紧致的;compact set：紧致集合; compact space：紧致空间; complement：补集或补运算; completelattice：完备格; complete metric space：完备的度量空间; complete space：完备空间; complexmanifold：复流形; complex plane：复平面; congruence：同余; congruent：全等; connectedspace：连通空间; constructible universe：可构造全集; constructions of the real numbers：实数的构造; continued fraction：连分数; continuous：连续; continuum hypothesis：连续统假设;contractible space：可缩空间; convergence space：收敛空间; cosine：余弦; countable：可数;countable set：可数集; cross product：叉积; cycle space：圈空间; cyclic group：循环群;Dde Morgan's laws：德·摩根律; Dedekind completion：戴德金完备性; Dedekind cut：戴德金分割;del：微分算子; dense：稠密; densely ordered：稠密排列; derivative：导数; determinant：行列式; diffeomorphism：可微同构; difference：差; differentiablemanifold：可微流形;differential calculus：微分学; dimension：维数; directed graph：有向图; discrete space：离散空间; discriminant：判别式; distance：距离; distributivity：分配律; dividend：被除数;dividing：除; divisibility：整除; division：除法; divisor：除数; dot product：点积;Eeigenvalue：特征值; eigenvector：特征向量; element：元素; elementary algebra：初等代数;empty function：空函数; empty set：空集; empty product：空积; equal：等于; equality：等式或等于; equation：方程; equivalence relation：等价关系; Euclidean geometry：欧几里德几何;Euclidean metric：欧几里德度量; Euclidean space：欧几里德空间; Euler's identity：欧拉恒等式;even number：偶数; event：事件; existential quantifier：存在量词; exponential function：指数函数; exponential identities：指数恒等式; expression：表达式; extended real number line：扩展的实数轴;Ffalse：假; field：域; finite：有限; finite field：有限域; finite set：有限集合; first-countablespace：第一可数空间; first order logic：一阶逻辑; foundations of mathematics：数学基础;function：函数; functional analysis：泛函分析; functional predicate：函数谓词;fundamental theorem of algebra：代数基本定理; fraction：分数;Ggauge space：规格空间; general linear group：一般线性群; geometry：几何学; gradient：梯度;graph：图; graph of a relation：关系图; graph theory：图论; greatest element：最大元;group：群; group homomorphism：群同态;HHausdorff space：豪斯多夫空间; hereditarily finite set：遗传有限集合; Heron's formula：海伦公式; Hilbert space：希尔伯特空间;Hilbert's axioms：希尔伯特公理系统; Hodge decomposition：霍奇分解; Hodge Laplacian：霍奇拉普拉斯算子; homeomorphism：同胚; horizontal：水平;hyperbolic function identities：双曲线函数恒等式; hypergeometric function identities：超几何函数恒等式; hyperreal number：超实数;Iidentical：同一的; identity：恒等式; identity element：单位元; identity matrix：单位矩阵;idempotent：幂等; if：若; if and only if：当且仅当; iff：当且仅当; imaginary number：虚数;inclusion：包含; index set：索引集合; indiscrete space：非离散空间; inequality：不等式或不等; inequality of arithmetic and geometric means：平均数不等式; infimum：下确界; infiniteseries：无穷级数; infinite：无穷大; infinitesimal：无穷小; infinity：无穷大; initial object：初始对象; inner angle：内角; inner product：内积; inner product space：内积空间; integer：整数; integer sequence：整数列; integral：积分; integral domain：整数环; interior：内部;interior algebra：内部代数; interior point：内点; intersection：交集; inverse element：逆元;invertible matrix：可逆矩阵; interval：区间; involution：回旋; irrational number：无理数;isolated point：孤点; isomorphism：同构;JJacobi identity：雅可比恒等式; join：并运算;K格式： Kuratowski closure axioms：Kuratowski 闭包公理;Lleast element：最小元; Lebesgue measure：勒贝格测度; Leibniz's law：莱布尼茨律; Liealgebra：李代数; Lie group：李群; limit：极限; limit point：极限点; line：线; line segment：线段; linear：线性; linear algebra：线性代数; linear operator：线性算子; linear space：线性空间; linear transformation：线性变换; linearity：线性性; list of inequalities：不等式列表; list oflinear algebra topics：线性代数相关条目; locally compact space：局部紧致空间; logarithmicidentities：对数恒等式; logic：逻辑学; logical positivism：逻辑实证主义; law of cosines：余弦定理; L??wenheim-Skolem theorem：L??wenheim-Skolem 定理; lower limit topology：下限拓扑;Mmagnitude：量; manifold：流形; map：映射; mathematical symbols：数学符号; mathematicalanalysis：数学分析; mathematical proof：数学证明; mathematics：数学; matrix：矩阵;matrix multiplication：矩阵乘法; meaning：语义; measure：测度; meet：交运算; member：元素; metamathematics：元数学; metric：度量; metric space：度量空间; model：模型; modeltheory：模型论; modular arithmetic：模运算; module：模; monotonic function：单调函数;multilinear algebra：多重线性代数; multiplication：乘法; multiset：多样集;Nnaive set theory：朴素集合论; natural logarithm：自然对数; natural number：自然数; naturalscience：自然科学; negative number：负数; neighbourhood：邻域; New Foundations：新基础理论; nine point circle：九点圆; non-Euclidean geometry：非欧几里德几何; nonlinearity：非线性; non-singular matrix：非奇异矩阵; nonstandard model：非标准模型; nonstandardanalysis：非标准分析; norm：范数; normed vector space：赋范向量空间; n-tuple：n 元组或多元组; nullary：空; nullary intersection：空交集; number：数; number line：数轴;Oobject：对象; octonion：八元数; one-to-one correspondence：一一对应; open：开集; openball：开球; operation：运算; operator：算子; or：或; order topology：序拓扑; ordered field：有序域;ordered pair：有序对; ordered set：偏序集; ordinal number：序数; ordinarymathematics：一般数学; origin：原点; orthogonal matrix：正交矩阵;Pp-adic number：p进数; paracompact space：仿紧致空间; parallel postulate：平行公理;parallelepiped：平行六面体; parallelogram：平行四边形; partial order：偏序关系; partition：分割; Peano arithmetic：皮亚诺公理; Pedoe's inequality：佩多不等式; perpendicular：垂直;philosopher：哲学家; philosophy：哲学; philosophy journals：哲学类杂志; plane：平面; pluralquantification：复数量化; point：点; Point-Line-Plane postulate：点线面假设; polarcoordinates：极坐标系; polynomial：多项式; polynomial sequence：多项式列; positive-definitematrix：正定矩阵; positive-semidefinite matrix：半正定矩阵; power set：幂集; predicate：谓词; predicate logic：谓词逻辑; preorder：预序关系; prime number：素数; product：积;proof：证明; proper class：纯类; proper subset：真子集; property：性质; proposition：命题; pseudovector：伪向量; Pythagorean theorem：勾股定理;QQ.E.D.：Q.E.D.; quaternion：四元数; quaternions and spatial rotation：四元数与空间旋转;question：疑问句; quotient field：商域; quotient set：商集;Rradius：半径; ratio：比; rational number：有理数; real analysis：实分析; real closed field：实闭域; real line：实数轴; real number：实数; real number line：实数线; reflexive relation：自反关系; reflexivity：自反性; reification：具体化; relation：关系; relative complement：相对补集;relatively complemented lattice：相对补格; right angle：直角; right-handed rule：右手定则;ring：环;Sscalar：标量; second-countable space：第二可数空间; self-adjoint operator：自伴随算子;sentence：判断; separable space：可分空间; sequence：数列或序列; sequence space：序列空间; series：级数; sesquilinear function：半双线性函数; set：集合; set-theoretic definitionof natural numbers：自然数的集合论定义; set theory：集合论; several complex variables：一些复变量; shape：几何形状; sign function：符号函数; singleton：单元素集合; social science：社会科学; solid geometry：立体几何; space：空间; spherical coordinates：球坐标系; squarematrix：方块矩阵; square root：平方根; strict：严格; structural recursion：结构递归;subset：子集; subsequence：子序列; subspace：子空间; subspace topology：子空间拓扑;subtraction：减法; sum：和; summation：求和; supremum：上确界; surreal number：超实数; symmetric difference：对称差; symmetric relation：对称关系; system of linearequations：线性方程组;Ttensor：张量; terminal object：终结对象; the algebra of sets：集合代数; theorem：定理; topelement：最大元; topological field：拓扑域; topological manifold：拓扑流形; topological space：拓扑空间; topology：拓扑或拓扑学; total order：全序关系; totally disconnected：完全不连贯;totally ordered set：全序集; transcendental number：超越数; transfinite recursion：超限归纳法; transitivity：传递性; transitive relation：传递关系; transpose：转置; triangleinequality：三角不等式; trigonometric identities：三角恒等式; triple product：三重积; trivialtopology：密着拓扑; true：真; truth value：真值;Uunary operation：一元运算; uncountable：不可数; uniform space：一致空间; union：并集;unique：唯一; unit interval：单位区间; unit step function：单位阶跃函数; unit vector：单位向量;universal quantification：全称量词; universal set：全集; upper bound：上界;Vvacuously true：??; Vandermonde's identity：Vandermonde 恒等式; variable：变量;vector：向量; vector calculus：向量分析; vector space：向量空间; Venn diagram：文氏图;volume：体积; von Neumann ordinal：冯·诺伊曼序数; von Neumann universe：冯·诺伊曼全集;vulgar fraction：分数;ZZermelo set theory：策梅罗集合论; Zermelo-Fraenkel set theory：策梅罗-弗兰克尔集合论; ZF settheory：ZF 系统; zero：零; zero object：零对象;下载全文。

第一部分英汉微积分词汇Part1 English-Chinese Calculus V ocabulary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step 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period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constant 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 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 of limits收敛数列的有界性 boundedness of aconvergent sequence子列 subsequence函数的极限 limits of functions函数()f x 当x 趋于x 0时的极限 limit of functions ()f x as x approaches x 0 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 sequence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 等阶无穷小 equivalent infinitesimal 函数的连续性 continuity of a function 增量 increment函数()f x 在x 0连续 the function ()f x is continuous at x 0左连续 left continuous 右连续 right continuous区间上的连续函数 continuous function 函数()f x 在该区间上连续 function ()f x 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 thesecond 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 minimum)零点定理 the zero point theorem 介值定理 intermediate value theorem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 derivative 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()f x 在闭区间【a,b 】上可导 ()f x isderivable 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differential 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stable 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被积函数integrand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 with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 ofintegrals函数在区间上的平均值average value of a function on an integvals牛顿－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improper 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椭圆ellipse旋转体的面积volume of 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parallel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direction 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旋转双叶双曲面revolution 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 revolution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 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 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第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Application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 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 existenceof implicit function曲线的切向量tangent vector of 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 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 integral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 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 first 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收敛半径radius of convergence收敛区间interval 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 component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 equation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衰变decay齐次方程homogeneous equation一阶线性方程linear differential equation 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 higher 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 differential equation with variable 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 damping 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常系数线性微分方程组system of linera differential equations with constant coefficient。

数学分析中的英语单词第一章real number and its properties 实数及其性质 rational number 有理数 irrational number 无理数 definition 定义 proposition 命题plus 加minus 减multiplied by/times 乘over/is to/divided by 除absolute value and inequality 绝对值与不等式 triangle inequality 三角不等式 inverse triangle inequality 反三角不等式 Bernoulli inequality 伯努利不等式 principles of supremum and infimum 确界原理open interval 开区间closed interval 闭区间semi-open interval 半开区间semi-closed interval 半闭区间finite interval 有限区间 infinite interval 无限区间 neighborhood 领域deleted neighborhood 去心邻域sum 和difference 差product 积quotient 商number axis/number line 数轴 closeness 封闭性 Archimedean property 阿基米德性质 density 稠密行upper and lower bounds 上界和下界 bounded set 有界集 unbounded set 无界集 existence domian 存在域 supremum 上确界 infimum 下确界order-complete set 有序完备集 completeness of real numbers 实数的完备性 complete ordered field 全序域 axiom of completeness 完备性公理 Dedekind cut 戴德金分割 Dedekind property 戴德金性质 constant and variable quantities 常量与变量 definition of function 函数的定义域 domain 定义域 range 值域 independent variable 自变量 dependent variable 因变量 intermediate variable 中间量 elementary function 初等函数 constant function 常量函数 power function 幂函数 exponential function 指数函数 logarithmic function 对数函数 trigonometric function 三角函数 inverse trigonometric function 反三角函数 compound function 复合函数 mapping 映射inverse mapping 逆映射 image 像primary image 原像 piecewise function 分段函数sign function 符号函数 Dirichlet function 狄利克雷函数 Riemann function 黎曼函数 bounded function 有界函数 monotone function 单调函数 monotone increasing function 单调增函数 strictly monotone function 严格单调函数 odd(even) function 奇函数（偶函数） minimal positive period 最小正周期 absolute value function 绝对值函数 identity function 恒等函数 polynomial function 多项式函数linear function 线性函数 quadratic function 二次函数rational function 有理函数 hyperbolic sine 双曲正弦 hyperbolic cosine 双曲余弦 trigonometric identity 三角恒等式odd-even identity 奇偶恒等式 cofunction identity 余函数恒等式 Pythagorean identity 毕达哥拉斯恒等式 half-angle identity 半角恒等式 product identity 积恒等式sum identity 和恒等式 addition identity 加法恒等式 double-angle identity 倍角恒等式第二章 数列极限limit of sequence 数列极限 divergent sequence 发散数列 infinitesimal sequence 无穷小数列 convergent sequence 收敛数列 uniqueness theorem 唯一性定理boundedness theorem 有界性定理 inheriting order properties 保序性inheriting inequality 保不等式 subsequence 子列strictly increasing 严格递增 monotone increasing sequence 单调递增序列 monotone decreasing sequence 单调递减序列 necessary condition 必要条件sufficient condition 充分条件squeeze principle 夹逼定理Cauchy convergence criterion 柯西收敛准则第三章 函数极限limit of function 函数极限infinite limit 无穷极限one-sided limit 单侧极限right(left)limit/right(left) hand limit 右（左）极限 property of limit of function 函数极限的性质 local boundedness 局部有界性Heine theorem 海涅定理infinity 无穷大量order of infinitesimal 无穷小量的阶 infinitesimal of higher(lower) order 高（低）阶无穷小量 infinitesimal of same order 同阶无穷小量 equivalent infinitesimal 等价无穷小量k-order infinitesimal k-阶无穷小量 vertical asymptote 垂直渐近线oblique asymptote 斜渐进线 horizontal asymptote 水平渐近线第四章函数的连续性increment of independent variable 自变量的增量 increment of function 函数的增量right(left) continuous 右(左)连续discontinuity point and its classification 间断点及其分类 removable discontinuity 可去间断点jump discontinuity 跳跃间断点 discontinuity of the first kind 第一类间断点 discontinuity of the second kind 第二类间断点local properties of continuous function 连续函数的局部性质 composition properties of continuous function 连续函数的复合性质闭区间上连续函数的性质 properties of continuous function over closedintervalextreme value theorem 极值定理maximum and minimum value theorem 最大值和最小值定理 intermediate value theorem 介值性定理zero-point theorem 零点定理uniform continuity theorem 一致连续定理continuity of inverse function 反函数的连续性local inheriting order property 局部保号性continuity of elementary function 初等函数的连续性第五章 导数和微分finite increment formula 有限增量公式rate of change 变化率difference quotient 差商left(right) derivative 左（右）导数 derivative function 导函数derivable function 可导函数geometric meaning of derivative 导数的集合意义Fermat theorem 费马定理Darboux theorem 达布定理intermediate value theorem of derivative function 导函数的介值定理 algebra of derivatives 导数的四则运算 derivative of sum 和的导数derivatives of difference 差的导数derivative of product 积的导数derivative of quotient 商的导数 derivative of inverse function 反函数的导数 maximum value 最大值minimum value 最小值 derivative of composite function 复合函数的导数 logarithmic derivative 对数求导法 parametric equation of circle 圆的参数方程 parametric equation of ellipse 椭圆的参数方程 parametric equation of cycloid 摆线的参数方程 parametric equation of asteroid 星形线的参数方程 second derivative 二阶导数third derivative 三阶导数n-th derivative n阶导数Leibniz formula 莱布尼茨公式 acceleration 加速度physical interpretation 物理解释 concept of differential 微分的概念 differentiable function 可微函数linear principal part 线性主部 differential of independent variable 自变量的微分 operational rules of differential 微分的运算法则 invariance of differential form 微分形式的不变性 geometric meaning of differential 微分的几何意义 higher-order differential 高阶微分第六章 微分中值定理Rolle mean value theorem 罗尔中值定理 Lagrange mean value theorem 拉格朗日中值定理 Cauchy mean value theorem 柯西中值定理 Taylor theorem 泰勒定理L’Hospital rule 洛必达法则limit of indeterminate form of type 0/0 0/0型不定式极限 indeterminate form of type ∞/∞ ∞/∞型不定式other indeterminate forms 其他类型不定式Taylor formula with Peano remainder 带有皮亚诺型余项的泰勒公式Taylor coefficient 泰勒系数Taylor polynomial 泰勒多项式remainder of Taylor formula 带有拉格朗日型余项的泰勒公式Taylor formula with Lagrange remainder 带有拉格朗日型余项的麦克劳林公式extreme value of function 函数的极值test of extreme value 极值判断the first sufficient condition of extreme value 极值的第一充分条件 convexity and inflection point of function 函数的凸性和拐点 convex function 凸函数concave function 凹函数strictly convex function 严格凸函数strictly concave function 严格凹函数Jenson inequality 琴生不等式第七章实数的完备性实数击完备性的基本定理 fundamental theorems of completeness in the setof real numbersnested interval theorem 闭区间套定理Cauchy convergence criterion 柯西收敛准着 accumulation theorem 聚点定理finite covering theorem 有限覆盖定理upper and lower limits 上极限和下极限第八章 不定积分indefinite integral 不定积分primitive function 原函数integrand function 被积函数integral sign 积分符号expression of integrand 积分表达式integral constant 积分常数table of basic integrals 基本积分表 geometric meaning of indefinite 不定积分的几何意义 integral curve 积分曲线initial condition 初始条件 integration by parts 分部积分法 integration by substitutions 换元积分法formula of substitution of the first kind 第一换元公式 indefinite integral of rational function 有理函数的不定积分 proper fraction 真分式improper fraction 假分式 decomposition into partial fractions 部分分式分解 method of undermined coefficients 待定系数法第九章 定积分definite integral 定积分curvilinear trapezoid 曲边梯形dividing/partition 分割norm/modulus 模Riemann sum 黎曼和Riemann integral 黎曼积分 integrability in the sense of Riemann 黎曼可积interval of integration 积分区间upper and lower limits 上限和下限 geometric meaning of definite integral 定积分的几何意义 upper sum 上和lower sum 下和Darboux upper sum 达布上和Darboux lower sum 达布下和Newton-Leibniz formula 牛顿-莱布尼茨公式 necessary condition for integrability 可积的必要条件 necessary and sufficient conditions for integrability 可积的充要条件 integrable function class 可积函数类linear property of definite integral 定积分的线性性质 additive with respect to integral interval/additivityover integral interval积分区间的可加性 mean value theorem of integral 积分中值定理 average value 平均值integral with variant upper limit 变上限积分 existence of primitive function 原函数的存在性 integration by substitution 换元积分法 integration by parts 分部积分法integral form of reminder of Taylor formula 泰勒公式的积分类型 第十章 定积分的应用area of plane figure 平面图形的面积method of finding volume of a solid from the knows area of parallel sections 由平行截面面积求体积的方法arc length and curvature of plane curve 平面的曲线的弧长与曲率 smooth curve 光滑曲线differential of arc 弧微分circle of curvature 曲率圆radius of curvature 曲率半径area of revolution surface 旋转曲面的面积some applications of definite integral in physics 定积分在物理中的某些应用gravitation 引力work 功approximate computation of definite integral 定积分的近似计算 trapezoidal method 梯形法parabola method 抛物线法第十一章反常积分notion of improper integral 反常积分的概念 improper integral on infinite interval 无穷区间上的反常积分 improper integral of unbounded function 无界函数的反常积分 property of infinite integral and test of 无穷积分的性质和收敛判convergence 别absolutely convergent 绝对收敛comparison test 比较收敛法Cauchy test 柯西判别法Dirichlet test 狄利克雷判别法Abel test 阿贝尓判别法第十二章数项级数series with number terms 数项级数infinite series 无穷级数convergence of series 级数的收敛性 sequence of partial sum 部分和序列geometric series 几何级数harmonic series 调和级数Cauchy convergence criterion for series 级数收敛的柯西准则 series with positive terms 正项级数necessary condition for convergence 收敛的必要条件root test 根式判别法D’alembert(ratio) test 达朗贝尔判别法（比式判别法）limit form of ratio test 比式判别法的极限形式 Gauss test 高斯判别法integral test 积分判别法Raabe test 拉贝尓判别法p-series p级数series with arbitraty terms 一般项级数alternating series 交错级数Leibnitz test 莱布尼茨判别法 rearrangement of series 级数的重排Abel test 阿贝尓判别法Dirichlet test 狄利克雷判别法第十章 函数列与函数项级数convergent at x"在点x"收敛convergence domain/region of convergence 收敛域sum function 和函数limit function 极限函数series of functions 函数项级数uniform convergence 一致收敛test of uniform convergence 一致收敛判别法魏尔斯特拉判别法 Weierstrass’s test/Weierstrass uniformconvergence criterion/Weierstrass m-test foruniform convergenceuniform boundedness 一致有界Dirichlet test 狄利克列判别法第十四章幂级数power series 幂级数interval of convergence 收敛区间radius of convergence 收敛半径Abel theorem 阿贝尓定理operations of power series 幂级数的运算taylor series 泰勒级数expansion of power series of elementary function 初等函数的幂级数展开式 exponential function of complex variable 复变量的指数函数Euler formula 欧拉公式第十五章傅里叶级数Fourier series 傅里叶级数 trigonometric series 三角级数system of orthogonal functions 正交函数系simple harmonic vibration 简谐振动Fourier series for function of period 2π以2π为周期的函数的傅立叶级数angular frequency 角频率piecewise smooth 分段光滑Fourier coefficient 傅立叶系数 convergence theorem 收敛定理Fourier series of even and odd functions 奇函数与偶函数的傅立叶级数amplitude 振幅sine series 正弦级数cosine series 余弦级数periodic extension 周期延拓第十六章多元函数的极限与连续functions of several variables 多元函数plane point set 平面点集coordinate plane 坐标平面interior point 内点outer point 外点boundary point 界点boundary 边点isolated point 孤立点open set 开集closed set 闭集connectedness 连通性connected open set 连通开集open domain(region) 开域closed domain(region) 闭域bounded point set 有界点集unbounded point set 无界点集nested closed domain theorem 闭域套定理function of two variables 二元函数n-dimensional vector space n-维向量空间improper limit 非正常极限double limit 二重极限properties of continuous functions on bounded closed region 有界闭区域上连续函数的性质repeated limits 累次极限 total increment 全增量partial increment 偏增量第十七章多元函数微分学total differential 全微分partial derivative 偏导数continuously differentiate 连续可微tangent plane of surface 曲面的切平面normal plane of curve 曲线的法平面 differentiation of composite function 复合函数微分法chain rule for functions of several variables 多元函数的链式法则 invariance of differential form of first order 一阶微分形式的不变性 directional derivative and gradient 方向导数与梯度 differentiability 可微性Taylor formula 泰勒公式problem of extreme value 极值问题partial derivative of higher order 高阶偏导数mixed partial derivative 混合偏导数第十八章隐函数定理及其应用existence and uniqueness theorem of implicit隐函数存在唯一性定理 functionssystem of implicit functions 隐函数组functional determinant (Jacobian determinant) 函数行列式（雅可比行列式）system of inverse functions 反函数组coordinate transformation 坐标变换geometrical application 几何应用tangent line and normal line of plane curve 平面曲线的切线与法线 tangent line and normal plane of space curve 空间曲线的切线与法平面 conditional extremum 条件极值Lagrange multiplier method 拉格朗日乘数法第十九章 含参变量积分proper integral with parameter 含参量的正常积分 improper integral with parameter 含参量的反常积分Euler integral 欧拉积分 Weierstrass test 魏尔斯特拉判别法 Dicichlet test 狄利克雷判别法 improper integral with infinite bound 无穷限的反常积分 improper integral with unbounded 无界函数的反常积分 Gamma functionBeta function第二十章inner area 内面积outer area 外面积cylindrical body with tip surface 曲顶柱体fineness 细度integral region 积分区域double integral 二重积分x-type region x型区域y-type region y型区域triple integral 三重积分change of variable in triple integral 三重积分换元法 transformation of cylindrical 柱面坐标变换 transformation of spherical coordinates 球面坐标变换area of surface 曲面面积第十一章曲线积分第一型曲线积分 curvilinear integrals of the first kind/line integrationof 1-form第二型曲线积分 curvilinear integrals of the first kind/line integrationof 2-formrelation between two classes of curvilinear两次曲线积分的联系 integralsGreen formula 格林公式 independence of curvilinear integrals with曲线积分与路径无关性 pathsimple connected region 单连通区域complex connected region 复连通区域第二十二章曲面积分surface integral of the first kind 第一型曲面积分 surface integral of the second kind 第二型曲面积分 unilateral surface 单侧曲面bilateral surface/two sided face 双侧曲面right-hand rule 右手法则relation between two classes of surface integrals 两类曲面积分的关系 Gauss formula 高斯公式Stokes formula 斯托克斯公式 introduction to field 场论初步field of vectors 向量场gradient field 梯度场gravitation field 引力场divergence field 散度场rotation field 旋度场circulation 环流量。

微积分英⽂词汇,⾼数名词中英⽂对照,⾼等数学术语英语翻译⼀览V、X、Z:Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平⾯Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三⾓函数Trigonometric integrals ：三⾓积分Trigonometric substitutions ：三⾓代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：⼆阶导数Second Derivative Test ：⼆阶导数试验法Second partial derivative ：⼆阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲⾯Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球⾯坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲⾯Surface integral ：⾯积分Surface of revolution ：旋转曲⾯Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直⾓坐标Rectangular coordinate system ：直⾓坐标系Relative maximum and minimum ：相对极⼤值与极⼩值Revenue function ：收⼊函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲⾯Riemann Sum ：黎曼和Riemannian geometry ：黎曼⼏何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱⾯Paraboloid ：抛物⾯Parallelepiped ：平⾏六⾯体Parallel lines ：并⾏线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分⽅程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平⾯Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极⽅程式Pole ：极点Polynomial ：多项式Positive angle ：正⾓Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极⼤与极⼩值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘⼦Natural exponential function ：⾃然指数函数Natural logarithm function ：⾃然对数函数Natural number ：⾃然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分⽅程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最⼩上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等⾼线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性⽅程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平⾯上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基⼏何Local extremum ：局部极值Local maximum and minimum ：局部极⼤值与极⼩值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：⾃变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：⽆穷极限Infinite series ：⽆穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三⾓函数Iterated integral ：逐次积分H:Higher mathematics ⾼等数学/⾼数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：⽅程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：⼀阶导数试验法First octant ：第⼀卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：⼏何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半⾓公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：⾼阶导数Horizontal asymptote ：⽔平渐近线Horizontal line ：⽔平线Hyperbola ：双曲线Hyper boloid ：双曲⾯D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：⽅向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：⾼阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：⼆阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：⾏列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分⽅程partial ：偏微分⽅程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：⽅向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：⼆重积分change of variable in ：⼆重积分之变数变换in polar coordinates ：极坐标⼆重积分C:Calculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡⼉坐标⼀般指直⾓坐标Cartesian coordinates system ：笛卡⼉坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在⼀点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡⼉坐标cylindrical ：柱⾯坐标polar ：极坐标rectangular ：直⾓坐标spherical ：球⾯坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平⾯Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、B:Absolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极⼤与极⼩Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：⽤微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：⾯积under a curve ：曲线下⽅之⾯积between curves ：曲线间之⾯积in polar coordinates ：极坐标表⽰之⾯积of a sector of a circle ：扇形之⾯积of a surface of a revolution ：旋转曲⾯之⾯积Asymptote ：渐近线horizontal ：⽔平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：⼆项级数关键词：微积分英⽂,⾼等数学英⽂翻译,⾼数英语词汇。

计量经济学常用英语词汇，都在这里了！计量经济学常用英语词汇集锦Absolute deviation, 绝对离差Absolute residuals, 绝对残差Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition theorem, 加法定理Additive Noise, 加性噪声Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Alpha factoring,α因子法Alternative hypothesis, 备择假设Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis Of Effects, 效应分析Analysis Of Variance, 方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Angular transformation, 角转换ANOVA Models, 方差分析模型Arcsine transformation, 反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arrhenius relation, 艾恩尼斯关系Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Autocorrelation of residuals, 残差的自相关Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Case-control study, 病例对照研究Categorical variable, 分类变量Cauchy distribution, 柯西分布Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Auto matic Interaction Detector, 卡方自动交互检测Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Error Bar, 均值相关区间图Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor score, 因子得分Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fatality rate, 病死率Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查Generalized least squares, 综合最小平方法GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误。

高等数学 (Higher Mathematics) 一些基本名词中英文对照表中文英文中文英文函数function 逆时针方counterclockwise向定义域domain of definition 变量variable值域range of function 常量constant quantity 极限limit 坐标轴axis of coordinates 极限值limit value 横坐标abscissa发散diverge 纵坐标ordinate收敛converge 锐角acute angle连续性continuity 钝角obtuse angle连续函数continuous function 平角straight angle左连续continuity from the left 直角right angle开集open set 圆circle闭集closed set 半径radius闭区间closed interval 直径diameter区间interval 三角形triangle一元函数function of one variable 斜率slope多元函数function of several variables 无穷小infinitesimal内点inner point 无穷大infinite孤立点isolated point 正positive邻域neighborhood 负negative导数derivative 凸convex偏导数partial derivative 凹concave微分differential calculus 椭圆ellipse全微分total differential 双曲线hyperbola偏微分partial differential 曲线curve积分integral 曲面surface微积分infinitesimal calculus 交intersection重积分multiple integral 补集complement二重积分double integral 投影project三重积分threefold integral 等差级数arithmetical progression 中值定理law of the mean 几何级数geometric progression 极值extreme values 公理axioms定积分definite integral 定义definition不定积分indefinite integral 定理theorem曲线积分curvilinear integral 集合set曲面积分surface integral 元素element级数progression,series 空集empty数列sequence 子集subset微分方程differential equation 相等equal常微分方ordinary differential equation 常数constant程偏微分方partial differential equation 对数logarithm程差分方程difference equation 指数exponential特征方程characteristic equation 曲率curvature间断点discontinuity point 曲率圆circle of curvature渐近线asymptote 曲率半径radius of curvature切线tangent line 切平面tangent plane切线方程tangential equation 幂级数power series拐点point of inflexion 收敛半径convergence radius绝对收敛absolutely convergence 收敛区间convergence interval条件收敛conditional convergence 收敛区域convergence region和函数sum function 通解general solution解solution 特解special solution初始条件initial condition 阶order条件极值conditional extremum 常数项级constant series数必要条件necessary condition 正项级数positive series充分条件sufficient condition 交错级数alternate series 收敛判别convergence criterion 一般级数ordinary series 法比较判别comparison criterion法《线性代数》英文专业词汇英文中文Linear Algebra 线性代数determinant 行列式row 行column 列element 元素diagonal 对角线principal diagona 主对角线auxiliary diagonal 次对角线transposed determinant 转置行列式triangular determinants 三角行列式interchange 互换absolute value 绝对值identity 恒等式n-order determinants n 阶行列式evaluation of determinant 行列式的求值Algebra cofactor 代数余子式the Vandermonde determinant 范德蒙行列式method of Recursion relation 递推法induction 归纳法Cramer′s rule 克莱姆法则matrix 矩阵the zero matrix 零矩阵the identity matrix 单位矩阵symmetric 对称的英文中文skew-symmetric 反对称的commutative law 交换律square Matrix方阵a matrix of order m×n矩阵m×nthe determinant of matrix A方阵A的行列式operations on Matrices矩阵的运算a transposed matrix转置矩阵an inverse matrix逆矩阵an diagonal matrix对角矩阵an adjoint matrix伴随矩阵singular matrix奇异矩阵nonsingular matrix非奇异矩阵elementary transformations初等变换vectors向量components分量linearly combination线性组合space of arithmetical vectors向量空间subspace子空间dimension维basis基transformation matrix过渡矩阵linearly independent线性无关linearly dependent线性相关the minor of the k th order k 阶子式rank of a Matrix矩阵的秩row vectors行向量column vectors列向量the maximal linearly independent subsystem最大线性无关组Euclidean space欧几里德空间Unitary space酉空间英文中文systems of linear equations线性方程组elimination method消元法homogenous齐次的nonhomogenous非齐次的equivalent等价的necessary and sufficient condition充要条件incompatiable无解的unique solution唯一解the matrix of the coefficients系数矩阵general solution通解particular solution特解trivial solution零解nontrivial solution非零解the fundamental system of solutions基础解系eigenvalue特征值eigenvector特征向量characteristic polynomial特征多项式characteristic equation特征方程normed vector单位向量orthogonal正交的orthogonalization正交化the Gram-Schmidt process正交化过程reducing a matrix to the diagonal form对角化矩阵orthonormal basis标准正交基orthogonal transformation正交变换linear transformation线性变换quadratic forms二次型canonical form标准型the canonical form of a quadratic form二次型的标准型the second-order curve二次曲线coordinate transformation坐标变换。

实变函数与泛函分析教学大纲应用数学与信息计算等专业使用修订单位：山东财政学院统计与数理学院修订时间： 2009年8月修订课程中文名称：实变函数与泛函分析课程英文名称：Real Analysis and functional Analysis课程号：30001001学时数：68学分数：4先修课程：数学分析、线性代数适用专业：应用数学与信息计算等专业。

一、课程的性质和任务1. 课程性质《实变函数与泛函分析》是数学专业的一门专业基础课程。

《实变函数》课程结合抽象测度与积分理论, 介绍Lebesgue测度与Lebesgue积分的理论。

通过本课程的学习, 应使学生掌握测度论和实变函数论的基本理论和方法, 并且应用所学知识, 解决一些相关的理论和应用问题, 解决一些具有一定难度的习题。

同时, 通过本课程的学习, 要加深学生对数学分析课程中知识的理解, 培养学生严密的逻辑思维能力。

《泛函分析》课程是现代教学中的一门较新的数学分支，它综合地运用分析的，代数和几何的观点，方法研究分析数学中的许多问题，由它把具体的分析问题，由于它把具体的分析问题抽象到一种更加纯粹的代数拓扑结构的形式中进行研究，因此逐步形成了综合运用代数，几何平段处理问题的新方法，正因为这种纯粹形式的代数，拓扑结构是跟植于肥沃的经典分析和数学物理土壤之中的，所以由此发展起来的基本概念，定理和方法也就显的更为广泛，更为深刻，现在泛函分析已成为一门内容丰富，方法系统，体系完备，应用广泛的独立分支，通过该课程的学习，学生不仅能学到泛函分析的基本理论和方法，而且对学习其他数学分支以及把他应用到数理经济，现代控制论，量子场论，统计物理，工程技术等领域有很大帮助。

学生通过学习本课程，既能从较高的观点总结一、二年级学过的分析、代数中的有关概念、理论和方法，又能获得抽象思维和逻辑论证的进一步训练，为今后深入学习拓扑、微分方程、随机过程、最优化等现代数学各个学科提供基础。

实变函数与泛函分析教学大纲应用数学与信息计算等专业使用修订单位：山东财政学院统计与数理学院修订时间：2009年8月修订课程中文名称：实变函数与泛函分析课程英文名称：Real Analysis and functional Analysis 课程号：30001001学时数：68学分数：4先修课程：数学分析、线性代数适用专业：应用数学与信息计算等专业。

一、课程的性质和任务1. 课程性质《实变函数与泛函分析》是数学专业的一门专业基础课程。

《实变函数》课程结合抽象测度与积分理论, 介绍Lebesgue测度与Lebesgue积分的理论。

通过本课程的学习, 应使学生掌握测度论和实变函数论的基本理论和方法, 并且应用所学知识, 解决一些相关的理论和应用问题, 解决一些具有一定难度的习题。

同时, 通过本课程的学习, 要加深学生对数学分析课程中知识的理解, 培养学生严密的逻辑思维能力。

《泛函分析》课程是现代教学中的一门较新的数学分支，它综合地运用分析的，代数和几何的观点，方法研究分析数学中的许多问题，由它把具体的分析问题，由于它把具体的分析问题抽象到一种更加纯粹的代数拓扑结构的形式中进行研究，因此逐步形成了综合运用代数，几何平段处理问题的新方法，正因为这种纯粹形式的代数，拓扑结构是跟植于肥沃的经典分析和数学物理土壤之中的，所以由此发展起来的基本概念，定理和方法也就显的更为广泛，更为深刻，现在泛函分析已成为一门内容丰富，方法系统，体系完备，应用广泛的独立分支，通过该课程的学习，学生不仅能学到泛函分析的基本理论和方法，而且对学习其他数学分支以及把他应用到数理经济，现代控制论，量子场论，统计物理，工程技术等领域有很大帮助。

学生通过学习本课程，既能从较高的观点总结一、二年级学过的分析、代数中的有关概念、理论和方法，又能获得抽象思维和逻辑论证的进一步训练，为今后深入学习拓扑、微分方程、随机过程、最优化等现代数学各个学科提供基础。

高等数学(Higher Mathematics)一些基本名词中英文对照表中文英文中文英文函数function 逆时针方向counterclockwise定义域domain of definition 变量variable值域range of function 常量constant quantity极限limit 坐标轴axis of coordinates 极限值limit value 横坐标abscissa发散diverge 纵坐标ordinate收敛converge 锐角acute angle连续性continuity 钝角obtuse angle连续函数continuous function 平角straight angle左连续continuity from the left 直角right angle开集open set 圆circle闭集closed set 半径radius闭区间closed interval 直径diameter区间interval 三角形triangle一元函数function of one variable 斜率slope多元函数function of severalvariables无穷小infinitesimal内点inner point 无穷大infinite孤立点isolated point 正positive邻域neighborhood 负negative导数derivative 凸convex偏导数partial derivative 凹concave微分differential calculus 椭圆ellipse全微分total differential 双曲线hyperbola偏微分partial differential 曲线curve积分integral 曲面surface微积分infinitesimal calculus 交intersection 重积分multiple integral 补集complement 二重积分double integral 投影project三重积分threefold integral 等差级数arithmeticalprogression中值定理law of the mean 几何级数geometric progression极值extreme values 公理axioms定积分definite integral 定义definition 不定积分indefinite integral 定理theorem曲线积curvilinear integral 集合set分曲面积分surface integral 元素element 级数progression,series 空集empty 数列sequence 子集subset 微分方程differential equation 相等equal常微分方程ordinary differentialequation常数constant偏微分方程partial differentialequation对数logarithm差分方程difference equation 指数exponential特征方程characteristic equation 曲率curvature间断点discontinuity point 曲率圆circle of curvature 渐近线asymptote 曲率半径radius of curvature切线tangent line 切平面tangent plane切线方程tangential equation 幂级数power series拐点point of inflexion 收敛半convergence radius径绝对收敛absolutely convergence 收敛区间convergence interval条件收敛conditional convergence 收敛区域convergence region和函数sum function 通解general solution 解solution 特解special solution 初始条件initial condition 阶order条件极值conditional extremum 常数项级数constant series必要条件necessary condition 正项级数positive series充分条件sufficient condition 交错级数alternate series收敛判别法convergence criterion 一般级数ordinary series比较判别法comparison criterion。

初中函数中英文单词的含义大全总结以下是初中数学中常见的函数相关的英文单词及其含义：1. Function - 函数：一个将一个集合的元素映射到另一个集合的元素的规则，用来描述两个集合之间的依赖关系。

2. Domain - 域：函数中输入的元素所属的集合，通常用来表示自变量的取值范围。

3. Range - 值域／范围：函数中输出的元素所属的集合，也就是函数值的取值范围。

4. Input - 输入：函数中自变量的取值，也叫做自变量的"值"。

5. Output - 输出：函数中因变量的取值，也叫做函数的"值"。

6. Independent variable - 自变量：函数中独立变化的变量，通常是输入的元素。

7. Dependent variable - 因变量：函数中依赖自变量而变化的变量，通常是输出的元素。

8. Equation - 方程：一个等式，表示两个表达式相等的关系。

9. Linear function - 线性函数：一个一次方程所表示的函数，也叫做一次函数。

10. Quadratic function - 二次函数：一个二次方程所表示的函数。

11. Exponential function - 指数函数：一个以底数为常数，指数为自变量的函数。

12. Absolute value function - 绝对值函数：一个以自变量的绝对值为输入，以其实际值为输出的函数。

13. Piecewise function - 分段函数：一个函数根据给定的自变量值范围，使用不同的规则给出输出值。

14. Inverse function - 反函数：一个函数与另一个函数互为反函数，当两个函数的输入互为输出，输出互为输入时，它们互为反函数。

这些是初中数学中常见的函数相关的英文单词及其含义。

当然，数学中还有很多其他的函数名词，但以上是初学者常见的一些。

实变函数定义实分析（英语：real analysis，也称作实变函数论，英语：theory of real variable function）或实数分析是处理实数及实函数的数学分析。

专门实数函数及数列的解析特性，包括实数数列的极限，实函数的微分及积分、连续性，光滑性以及其他相关性质。

实分析常以基础集合论，函数概念定义等等开始。

有许多种将实数定义为有序域的方式。

合成的作法会提供许多实数的公理，将实数变成完备有序域。

在一般集合论的公理下，可以证明这些公理都是明确的，也就是说有一个公理的模型，任两个模型都是同构的。

这些模型中需要有一个有明确的定义，而大部分的模型都可以用实数为有序域时的基本性质来得到。

实数有许多重要的特性是和数学中格的定义有关，这些性质也是复数所没有的。

其中最重要的是，实数形成有序域，实数的有序满足反对称性、传递性及完全性，属于全序关系，而且实数有最小上限属性。

实数中的偏序关系带来了实变分析中许多重要的定理，例如单调收敛定理、介值定理及中值定理。

在实变分析中这些定理只针对实数，不过许多的结果可以应用在其他的数学对象（英语：mathematical object）。

特别是许多泛函分析及算子理论（英语：operator theory）中的概念是来自实数中概念的扩展，这类的扩展包括里斯空间（英语：Riesz space）及正算子（英语：positive operator）的理论。

也有数学家考虑复数数列的实部及虚部，例如算子数列的逐点评估（英语：strong operator topology）。

序列是一个定义域为可数全序集合的函数，多半会让定义域是自然数或是所有整数。

例如，一个实数的序列为以下定义的映射 a : N →R , n ↦a n {displaystyle a:mathbb {N} to mathbb {R} , nmapsto a_{n}} ，常会表示为( a n ) = ( a n ) n ∈N = ( a 1 , a 2 , a 3 , ⋯) {displaystyle (a_{n})=(a_{n})_{nin mathbb {N} }=(a_{1},a_{2},a_{3},cdots )} 。