数学分析英文词汇

1、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pri

2、nciples 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

3、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 quantit

4、ies 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

5、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

6、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Pythagore

7、an 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 or

8、der 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 lim

9、it 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

10、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 discon

11、tinuity 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properties of continuous function over closed 闭区间上连续函数的性质intervalextreme value theorem 极值定理maximum and min

12、imum 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differenc

13、e 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 differenc

14、e 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 cyclo

15、id 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

16、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LHospital rule

17、 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

18、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

19、不等式第七章实数的完备性fundamental theorems of completeness in the set 实数击完备性的基本定理of 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

20、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

21、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i

22、ntegrability 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 a

23、nd 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/additivity 积分区间的可加性over integral intervalmean value theorem of integral 积分中值定理average value 平均值integral with variant upper limit 变上

24、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 由平行截面面积求体积的knows area of parallel sections 方法arc length and cur

25、vature 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

26、 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Fourier series of even and odd functions 奇函数与偶函数的傅立叶级数amplitude 振幅sine seri

27、es 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

28、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 有界闭区域上连续函数的closed region 性质repeated limits 累次极限t

29、otal 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 di

30、fferential 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functions

31、system 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conditio

32、nal 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