中英文对照表按笔画排列教学内容

中英文对照表（按笔画排列）一画一一映射one to one mapping一阶（全）微分形式不变性（total）differential form invariance of first order 一致连续性uniform continuity一致连续（的）uniformly continuous一致连续性定理uniform continuity theorem一致收敛uniform convergence一致收敛的uniformly convergent一致收敛函数序列uniformly convergent sequence of functions一致有界的uniformly bounded一致有界原理uniform boundedness principle一致有界定理uniform boundedness theorem一致有界函数序列uniformly bounded sequence of functions一致有界级数uniformly bounded series一致有界集uniformly bounded set二画二元函数binary function二阶导数second derivative二重极限double limit几何级数geometric series三画三角函数trigonometric function三角函数表trigonometric table三角不等式triangle inequality三角级数trigonometric series下极限lower limit；inferior limit下和lower sum下限lower limit；lower edge下界lower bound下类lower class下积分lower integral下确界infimum；greatest lower bound上极限upper limit；superior limit上和upper sum上限upper limit；upper edge上界upper bound上类upper class上积分upper integral上确界supremum；least upper bound子集subset子序列subsequence四画开区间open interval开覆盖open cover开集open set开域open domain; open region无穷大infinitely great; infinity无穷大的阶order of infinity无穷大量infinitely large quantity无穷小infinitesimal无穷小的阶order of infinitesimals无穷小等价infinitesimals equivalence无穷小数列infinitesimal sequence of number无穷限反常积分infinite limit improper integral无穷积分infinite integral无穷级数infinite series无限开覆盖infinite open cover无限区间infinite interval无限区域infinite region无限维的infinite dimensional无界函数unbounded function无界集unbounded set无理数irrational number不可导underivativity不连续点discontinuous point; point of discontinuity 不定积分indefinite integral不定式indeterminate expression不动点原理fixed point principle区间interval区间套nested intervals区间套定理nested intervals theorem比较原则comparison principle比较法relative method切线方程tangential equation中间变量intermediate variable中值公式mean value formula中值定理mean value theorem内函数interior function内点interior point内部interior牛顿-莱布尼茨公式Newton-Leibniz formula牛顿切线法Newton tangents method反三角函数anti-trigonometric function; inverse trigonometric function; inverse circular function反函数inverse function反函数定理inverse function theorem反常积分improper integral介值性定理intermediate value theorem; location principle分划partition分段连续性piecewise continuity分段连续函数piecewise continuous function分段函数piecewise function分部积分法integration by parts分部求和公式summation by parts formula分割subdividing; segmentation; excision; section分量函数component function区域region; domain切平面tangent plane切点point of contact; point of tangency 双曲抛物面hyperbolic paraboloid双纽线lemniscate双侧曲面two sided surface方向导数directional derivative方邻域square neighborhood贝塞尔不等式Bessel inequality贝塔函数 -function五画正无穷大plus infinity可去间断点removable discontinuous point 可求长的rectifiable可求长性rectifiability可求积性squarability可导derivable可积integrable可微differentiable可微函数differentiable function左导数left derivative左邻域left neighborhood左极限left limit; limit on the left左连续left continuous; continuous on the left 右导数right derivative右邻域right neighborhood右极限right limit; limit on the right右连续right continuous; continuous on the right 凸函数convex function凸区域convex region归结原则resolution principle凹函数concave function凹区域concave region外积outer product外函数outer function外点outer point外微分exterior differentiation半开半闭区间half open half closed interval发散divergence对数求导法logarithm derivation method对数函数logarithmic function对数螺线logarithmic spiral平面点列plane point range平面点集plane point set正交orthogonal正交函数系system of orthogonal functions 正弦级数sine series正项级数positive term series右手法则right-hand rule边界boundary发散divergence六画有上界函数upper bounded function有下界函数lower bound function有限开覆盖finite open cover有限维的finite dimensional有限区间finite interval有限增量公式finite increment formula 有限覆盖定理finite cover theorem有界函数bounded function有界点集bounded set of points有界集bounded set有界数列bounded number sequence有理函数rational function有理数rational有势场potential field存在域domain of existence达布下和Darboux lower sum达布上和Darboux upper sum达布和Darboux sum光滑曲线smooth curve曲边梯形curved trapezoid曲率curvature曲率半径radius of curvature曲率圆circle of curvature曲率形式curvature form曲线的曲率curvature of a curve曲率张量curvature tensor曲率向量curvature vector曲顶柱体curved cylinder同阶无穷大量infinitely large quantity of the same order 同阶无穷小量infinitesimals quantity of the same order 因变量dependent variable自变量independent variable自变量增量increment of independent variable全序total order负无穷大minus infinity闭区间closed interval闭区间套nested closed intervals闭域closed region; closed domain闭集closed set导函数derived function导数derivative导数极限定理limit of derivative theorem收敛converge收敛区间convergence interval; interval of convergence收敛半径convergence radius收敛准则convergence criterion收敛点point of convergence收敛域convergence domain; convergence region向量vector向量场vector field向量函数vector function交错级数alternating series压缩映射原理contracting mapping principle全微分total differential全微分方程total differential equation; exact differential equation 全增量total increment优级数majorizing series优级数判别法majorizing series discriminance达朗贝尔判别法D'Alembert's ratio test七画麦克劳林公式Maclaurin formula严格凸函数strictly convex function严格凹函数strictly concave function严格单调函数strictly monotonic function极大值maximum value极小值minimum value极值extreme value极值点extreme point极坐标变换polar coordinates transformation极限limit连续continuous连续函数continuous function连通性connectivity; connectedness连续可微性continuous differentiability抛物线法parabola formula邻域neighborhood狄利克雷判别法Dirichlet principle; Dirichlet criterion狄利克雷函数Dirichlet function条件收敛conditional convergence条件极值extremum with a condition间断点discontinuous point初始条件initial condition初等函数elementary function局部有界性local boundedness局部保号性local sign-preserving局部利普希茨条件local Lipschitz condition阿基米德有序域Archimedically ordered field阿基米德性Archimedean余项remainder term余弦函数cosine function余集complementary set含参量积分integral with parameter含参量反常积分improper integral with parameter 阿贝尔引理Abel lemma阿贝尔判别法Abel criterion阿贝尔定理Abel theorem阿贝尔变换Abel transformation八画奇函数odd function偶函数even function拐点inflection point; point of inflection拉格朗日公式Lagrange formula拉格朗日余项Lagrange remainder term; Lagrange residual term 拉格朗日乘数法Lagrange multiplicator method拉格朗日函数Lagrange function拉贝判别法Raabe criterion非正常下确界improper infimum非正常上确界improper supremum非正常极限improper limit垂直渐近线vertical asymptote周期函数periodic function周期曲线periodic curves变下限的定积分definite integral of variable lower limit变上限的定积分definite integral of variable upper limit变化率rate of change变换transformation单侧导数one sided derivative单侧极限one sided limit单侧曲面one sided surface单值对应single valued correspondence单值函数single valued function单调有界定理monotonic bounded theorem 单调函数monotonic function单调数列monotonic number sequence单连通区域simply connected region单射injective mapping定义域domain定积分definite integral直积direct product直径diameter函数行列式functional determinant; jacobian 位势函数potential function法平面normal plane法线normal line孤立点isolated point细度fineness空心邻域hollow neighborhood和函数summable function欧拉公式Euler formula欧拉积分Euler integral九画弧长length of arc弧微分arc differential柯西中值定理Cauchy mean value theorem; mean value theorem of Cauchy 柯西判别法Cauchy attribute柯西准则Cauchy criterion指数函数exponential function映射mapping矩形法rectangle method复合函数composite function复连通区域complex connected region待定系数法undetermined coefficient method差商difference quotient逆映射inverse mapping逆变换inverse transformation面积area面积元素element of area绝对收敛absolute convergence绝对值absolute value柱面坐标变换cylinder coordinates transformation显函数explicit function泰勒公式T aylor formula泰勒级数T aylor series泰勒展开式Taylor expansion界点boundary point十画费马定理Fermat theorem根的存在定理existence theorem of root原函数primitive function原像preimage; primary image振幅amplitude换元积分法integration by substitution致密性定理compactness theorem积分区间integral interval积分曲线integral curve积分和integral sum积分变量integral variable积分型余项integral residual term积分常数integration constant积分中值定理integral mean value theorem值域range高阶无穷小量infinitesimals quantity of the higher order 高阶导数higher order derivative高阶微分higher order differential递增数列increasing number sequence递减数列decreasing number sequence被积函数integrand高斯公式Gauss formula调和harmonic调和级数harmonic series部分和partial sum部分和序列sequence of partial sums部分和函数列function sequence of partial sums 逐项微分differentiation term by term逐项积分integration term by term逐项地in terms by terms通项general term通项公式the formula of general term圆邻域circular neighborhood格林公式Green theorem根式判别法radical criterion十一画基本初等函数fundamental elementary function 基本周期fundamental period梯形法trapezoidal rule常量函数constant function符号函数sign functional斜渐近线oblique asymptote渐近线asymptote减函数decreasing function像image偏导函数partial derivative偏导数partial derivative偏增量partial increment隐函数implicit function隐函数定理implicit function theorem隐函数的存在性定理existence theorem of implicit function 混合偏导数mixed partial derivative球坐标变换spherical coordinates transformation梯度gradient累次极限repeated limit累次积分repeated integral距离distance十二画最大（小）值定理maximum（minimum）value theorem 链式法则chain rule幂函数power function超平面hyperplane傅里叶系数Fourier coefficient等价无穷小量equivalent infinitesimals quantity等比级数geometric series等值面contour surface等值矩阵contour matrix散度divergence斯托克斯公式Stokes formula雅可比行列式Jacobi determinant雅可比矩阵Jacobi matrix十三画及以上瑕点improper point瑕积分improper integral跳跃间断点jump discontinuous point稠密性denseness微分differential微积分学基本定理fundamental theorem of calculus微商differential coefficient; derivative微分中值定理differential mean value theorem; mean value theorem of differential数列number sequence数轴number axis截面面积sectional area聚点cluster point; accumulation point聚点定理cluster point theorem; accumulation point theorem 黑塞矩阵Hesse matrix模module稳定点stable point黎曼函数Riemann function黎曼积分Riemann integral黎曼和Riemann sum增函数increasing function增量increment。