数学分析中的英文单词和短语

1、数学分析中的英文单词和短语第一章实数集与函数Chapter 1Set of Real Numbers and Functions实数及其性质real numbe and its properties有理数rational number无理数irrational number定义definition命题proposition加plus减minus乘multiplied by/times除over/is to/divided by绝对值与不等式absolute value and inequality三角不等式triangle inequality反三角不等式inverse triangle in

2、equality伯努利不等式Bernoulli inequality确界原理principles of supremum and infimum开区间closed interval闭区间closed interval半开区间semi-open interval半闭区间semi-closed interval有限区间finite interval无限区间infinite interval邻域neighborhood去心邻域deleted neighborhood和sum差difference积product商quotient数轴number axis/number line封闭性closenes

3、s阿基米德性Archimedean property稠密性density上界与下届upper and lower bounds有界集bounded set无界集unbounded set存在域existence domain上确界supremum下确界infimum有序完备集实数的完备性全序域完备性公理戴德金分割戴德金性质常量与变量函数的定义定义域值域自变量因变量中间变量单调性初等函数常量函数幂函数指数函数对数函数三角函数反三角函数反函数复合函数映射逆映射像原像分段函数符号函数狄利克雷函数黎曼函数有界函数单调函数单调增函数严格单调函数奇（偶）函数最小正周期绝对值函数恒等函数多项式函数线性函数二

4、次函数有理函数order-complete set completeness of real numbers complete ordered field axiom of completeness Dedekind cutDedekind propertyconstant and variable quantities definition of function domainrangeindependent variabledependent variableintermediate variablemonotonicityelementary functionconstant funct

5、ionpower functionexponential functionlogarithmic functiontrigonometric functioninverse trigonometric functioninverse functioncompound functionmappinginverse mappingimageprimary imagepiecewise functionsign functionDirichlet functionRiemann functionbounded functionmonotone functionmonotone increasing

6、functionstrictly monotone functionodd(even) functionminimal positive periodabsolute value functionidentity functionpolynomial functionlinear functionquadratic functionrational function双曲正弦hyperbolic sine双曲余弦hyperbolic cosine三角恒等式trigonometric identity奇偶恒等式odd-even identity余函数恒等式cofunction identity毕达

7、哥拉斯恒等式Pythagorean identity半角恒等式half-angle identity积恒等式product identity和恒等式sum identity加法恒等式addition identity倍角恒等式double-angle identity第二章数列极限Chapter 2Limits of Sequences数列极限limit of sequence发散数列divergent sequence无穷小数列infinitesimal sequence收敛数列convergent sequence唯一性定理uniqueness theorem有界性定理boundednes

8、s theorem保序性inheriting order properties保不等式性inheriting inequality子列subsequence严格递增strictly increasing单调递增数列monotone increasing sequence单调递减数列monotone decreasing sequence严格递增strictly decreasing必要条件necessary condition充分条件sufficient condition夹逼定理squeeze principle柯西收敛准则Cauchy convergence critterion第三章函数

9、极限Chapter 3Limits of Functions函数极限limit of function无穷极限infinite limit单侧极限one-sided limit右（左）极限right(left) limit/right(left) hand limit函数极限的性质property of limit of function局部有界性local boundedness海涅定理Heine theorem无穷大量infinity无穷小量的阶order of infinitesimal高（低）阶无穷小量infinitesimal of higher(lower) order同阶无穷小量

10、infinitesimal of same order等价无穷小量equivalent infinitesimalk-阶无穷小量k-order infinitesimal垂直渐近线vertical asymptote斜渐近线oblique asymptote水平渐近线horizontal asymptote第四章函数的连续性Chapter 4Continuity of Functions自变量的增量increment of independent variable函数的增量increment of function右（左）连续right(left) continuous间断点及其分类disco

11、ntinuity point and its classification可去间断点removable discontinuity跳跃间断点jump discontinuity第一类间断点discontinuity of the first kind第二类间断点discontinuity of the second kind连续函数的局部性质local properties of continuous function连续函数的复合性质composition properties of continuous function闭区间上连续函数的properties of continuous f

12、unction over closed性质interval极值定理extreme value theorem最大值和最小值定理maximum and minimum value theorem介值性定理intermediate value theorem零点定理zero-point theorem一致连续性定理uniform continuity theorem反函数的连续性continuity of inverse function局部保号性local inheriting order property初等函数的连续性continuity of elementary function第五章导

13、数和微分Chapter 5Derivatives and Differentials有限增量公式finite increment formula变化率rate of change差商difference quotient左（右）导数left(right) derivative导函数derivative function可导函数derivable function导数的集合意义geometric meaning of derivative费马定理Fermat theorem达布定理Darboux theorem导函数的介值定intermediatevaluetheoremof理derivativ

14、e function导数的四则运算algebra of derivatives和的导数derivative of sum差的导数derivative of difference积的导数derivative of product商的导数derivative of quotient反函数的导数derivative of inverse function最大值maximum value最小值minimum value复合函数的导数derivative of composite function对数求导法logarithmic derivative圆的参数方程parametric equation o

15、f circle椭圆的参数方程parametric equation of ellipse摆线的参数方程parametric equation of cycloid星形线的参数方parametric equation of asteroid程二阶导数second derivative三阶导数third derivativen 阶导数n-th derivative莱布尼茨公式Leibniz formula加速度acceleration物理解释physical interpretation微分的概念concept of differential可微函数differentiable function

16、线性主部linear principal part自变量的微分differential of independent variable微分的运算法则operational rules of differential微分形式的不变invariance of differential form性微分的几何意义geometric meaning of differential高阶微分higher-order differential第六章微分中值定理及其应用Chapter6MeanValueTheoremsofDifferentials and their Applications罗尔中值定理Rol

17、le mean value theorem拉格朗日中值定理Lagrange mean value theorem柯西中值定理Cauchy mean value theorem泰勒定理Taylor theorem洛必达法则l Hospittalrule0/0 型不定式极限limit of indeterminate form of type 0/0/ 型不定式indeterminate form of type/ 其它类型不定式other indeterminate forms带有皮亚诺型余项Taylor formula with Peano remainder的泰勒公式泰勒系数Taylor c

18、oefficient泰勒多项式Taylor polynomial泰勒公式的余项remainder of Taylor formula带有拉格朗日型余TaylorformulawithLagrange项的泰勒公式remainder带有拉格朗日型余MaclaurinformulawithLagrange项的麦克劳林公式remainder函数的极值extreme value of function极值判别test of extreme value极值的第一充分条the first sufficient condition of extreme件value函数的凸性和拐点convexityand in

19、flectionpoint offunction凸函数convex function凹函数concave function严格凸函数strictly convex function严格凹函数strictly concave function部分分式分解decomposition into partial fractions琴生不等式Jenson inequality待定系数法method of undetermined coefficients第七章实数的完备性第九章定积分Chapter 7Completeness of Real Numbers实数集完备性的fundamentaltheote

20、msof基本定理completeness inthe set ofrealnumbers区间套定理nested interval theorem柯西收敛准则Cauchy convergence criterion聚点定理accumulation theorem有限覆盖定理finite covering theorem上极限和下极限upper and lower limits第八章不定积分Chapter 8Indefinite Integrals不定积分indefinite integral原函数primitive function被积函数integrand function积分符号integr

21、al sign积分表达式expression of integrand积分常数integral constant基本积分表table of basic integrals不定积分的几何geometricmeaningofindefinite意义integral积分曲线integral curve初始条件initial condition分部积分法integration by parts换元积分法integration by substitution第一换元公式formula of substitution of the first kind有理函数的不定indefinite integral

22、of rational function积分真分式proper fraction假分式imiproper fractionChapter 9Definite Integrals定积分definite integral曲边梯形curvilinear trapezoid分割dividing/partition模norm/modulus黎曼和Riemann sum黎曼积分Riemann integral黎曼可积integrability in the sense of Riemann积分区间interval ofintegration上限和下限upper and lower limits定积分的几何

23、意义geometric meaning ofdefiniteintegral上和upper sum下和lower sum达布上和Darboux upper sum达布下和Darboux lower sum牛顿 -莱布尼茨公Newton-Leibniz formula式可积的必要条件necessary condition for integrability可积的充要条件necessary and sufficient conditionsfor integrability可积函数类integrable function class定积分的线性性质linear property of defini

24、te integral积分区间的可加性additive with respect tointegralinterval/additivityoverintegralinterval积分中值定理mean value theorem of integral平均值average value变上限积分integral with variant upper limit原函数的存在性existence of primitive function换元积分法integration by substitution分部积分法integration by parts泰勒公式的积分型integral form of

25、remainder ofTaylor余项formula第十章定积分的应用Chapter 10Applications of Definite Integrals平面图形的面积area of plane figure由平行截面面积method of finding volume of a solid求体积的方法fromtheknownareaofparallelsections平面曲线的弧长arc length and curvature of plane curve与曲率光滑曲线smooth curve弧微分differential of arc曲率圆circle of curvature曲率

26、半径radius of curvature曲率中心center of curvature旋转曲面的面积area of revolution surface定积分在物理中some applications of definite integral的某些应用in physics引力gravitation功work定积分的近似计approximate computation of definite算integral梯形法trapezoidal method抛物线法parabola method第十一章反常积分Chapter 11Improper Integrals狄利克雷判别法Dirichlet t

27、est阿贝尔判别法Abel test第十二章数项级数Chapter 12Series of Number Terms数项级数series with number terms无穷级数infinite series级数的收敛性convergence of series部分和序列sequence of partial sum几何级数geometric series调和级数harmonic series级数收敛的柯西Cauchy onvergence criterion for series准则正项级数series with positive terms收敛的必要条件necessary conditi

28、on for convergence根式判别法root test达朗贝尔判别法Dalembert(ratio) test（比式判别法）比式判别法的极limit form of ratio test限形式高斯判别法Gauss test积分判别法integral test拉阿伯判别法Raabe testp 级数p-series一般项级数series with arbitraty terms交错级数alternating series莱布尼茨判别法Leibnitz test级数的重排rearrangement of series阿贝尔判别法Abel test反常积分的概念无穷区间上的反常积分无界函数

29、的反常积分无穷积分的性质和收敛判别绝对收敛比较判别法柯西判别法notion of improper integralimproper integral on infinite intervalimproper integral of unbounded functionproperty of infinite integral and test of convergenceabsolutely convergentcomparison testCauchy test狄利克雷判别法Dirichlet test第十三章函数列与函数项级数Chapter13Sequences ofFunctionsa

30、ndSeries of Functions在点 x0 收敛convergent at x0收敛域convergencedomain/regionofconvergence和函数sum function极限函数limit function函数项级数series of functions一致收敛性uniform convergence一致收敛判别法test of uniform convergence维尔斯特拉斯判Weierstrasstest/sWeierstrass uniform别法convergencecriterion/Weierstrassm-test for uniform conv

31、ergence一致有界uniform boundedness狄利克雷判别法Dirichlet test正交函数系system of orthogonal functions简谐振动simple harmonic vibration以 2 为周期的Fourier series for functions of period 2函数的傅里叶级数角频率angular frequency分段光滑piecewise smooth傅里叶系数Fourier coefficient收敛定理convergence theorem奇函数与偶函数Fourierseriesofevenandodd的傅里叶级数func

32、tions振幅amplitude正弦级数sine series余弦级数cosine series周期延拓periodic extension第十四章幂级数Chapter 14Power Series幂级数power series收敛区间interval of convergence收敛半径radius of convergence阿贝尔定理Abel theorem幂级数的运算operations of power series泰勒级数taylor series初等函数的幂级expansion of powerseries of数展开式elementary function复变量的指数函expo

33、nential function ofcomplex数variable欧拉公式Euler formula第十五章傅里叶级数Chapter 15Fourier Series傅里叶级数Fourier series三角级数trigonometric series第十六章多元函数的极限与连续Chapter16LimitsandContinuityofFunctions of Several Variavles多元函数functions of several variables平面点集plane point set坐标平面coordinate plane内点interior point外点outer p

34、oint界点boundary point边界boundary孤立点isolated point开集open set闭集closed set连通性connectedness连通开集connected open set开域open domain(region)闭域closed domain(region)有界点集bounded point set无界点集unbounded point set闭域套定理nested closed domain theorem二元函数function of two variablesn-维向量空间n-dimensional vector space非正常极限impro

35、per limit二重极限double limit有界闭域上连续properties of continuous functions on函数的性质bounded closed region累次极限repeated limits全增量total increment偏增量partial increment第十八章隐函数定理及其应用Chapter 18 Implicit Funciton Theorems and their Applications第十七章多元函数微分学Chapter17DifferentialCalculusofFunctions of Several Variables全微分

36、total differential偏导数partial derivative连续可微continuously differentiable曲面的切平面tangent plane of surface曲线的法平面normal plane of curve复合函数微分法differentiation of composite function隐函数存在唯一性定理隐函数组函数行列式（雅可比行列式）反函数组坐标变换几何应用平面曲线的切线与法线空间曲线的切线与法平面条件极值拉格朗日乘数法existence and uniqueness theorem of implicit fucntionssyst

37、em of implicit functionsfunctional determinant (Jacobian determinant)system of inverse functionscoordinate transformationgeometrical applicationtangent line and normal line of plane curvetangent line and normal plane of space curveconditional extremumLagrange multiplier method多元函数的链式chain rule for f

38、ucntions of several法则variables一阶微分形式不invariance of differential form of first变性order方向导数与梯度directional derivative and gradient可微性differentialbility泰勒公式Taylor formula极值问题problem of extreme value高阶偏导数partial derivative of higher order混合偏导数mixed partial derivative第十九章含参量积分Chapter 19Integrals with Parameters含参量的正常积proper integral with parameter分含参量的反常积improper integral with parameter分欧拉积分Euler integral维尔斯特拉斯Weierstrass (m) test（M）判别法狄利