专业英语

单词2.1角angle维数dimension除divide除法division分数fraction高度height 利率interest rate长度length线段line segment同类量like quantity百分数percentage比例proportion商quotient比ratio速率speed项term单位unit宽width2.2锐角acute angle临边adjacent side角angle俯角angle of depression 仰角angle of elevation定义为be defined as表示成be denoted as全等congruence同终边的角conterminal angles初等几何elementary geometry勾股定理/毕达哥拉斯定理Gou-Gu theorem/Pythagoras theorem斜边hypotenuse 夹角included始边initial side余弦定理Law of cosines直角边leg互相依赖mutually dependent对边opposite side直角right angle angle解三角形solve a triangle三角形triangle三角学trigonometry 三角函数trigonometric function2.3分类classification公倍数common multiple合数composite可数的countable与矛盾contrary to整除:divide by整除性divisibility除法算式division equation辗转相除法Euclidean algorithm 有限集finite set最大公因数greatest common divisor无限的infinitely最小公倍数lowest common multiple正素因子positive prime divisor素数prime质因数prime factor/prime divisor过程process证明proof剩余remainder终止terminate 2.4抽象集abstract set上有界bounded above补集complement完备性公理completeness axiom组成comprise/constitute概念concept包含contain元素element/member交集intersection最小的上界least upper bound真子集proper subset集set子集subset术语terminology全集universe并集union 上界upper bound2.5竖直线vertical line水平线horizontal line数对pairs of numbers有序对ordered pairs纵坐标ordinate横坐标abscissas一一对应one-to-one 对应点corresponding points圆锥曲线conic sections非空图形non vacuous graph直立圆锥right circular cone定值角constant angle母线generating line双曲线hyperbola抛物线parabola椭圆ellipse退化的degenerate非退化的nondegenerate任意的arbitrarily相容的consistent在几何上geometrically二次方程quadratic equation判别式discriminant行列式determinant2.6向量vector单位向量unit vector法向量normal vector位置向量position vector基点base point向量的尖端tip of a vector向量的分量component of a vector点乘dot product参数方程parametric equation位移displacement 在集合上geometrical平行线parallel lines平行于parallel to平行四边形parallelogram不平行的nonparallel垂直的perpendicular指向point 点point加add 乘以multiply by2.7向量空间vector space行向量row vector列向量column vector线性相关linearly dependent线性无关linearly independent线性组合linear combination数量级scalar product矩阵matrix方阵square matrix行列式determinant逆矩阵inverse matrix单位矩阵identity matrix零矩阵zero matrix变换transformation到上的onto 同构isomorphism 同构的isomorphic 应用微分方程applied differential equations数理经济mathematicaleconomics量子力学quantum mechanics相容的consistent最终的ultimately 2.8函数关系function relation表格table反函数inverse function简单函数simple function特征函数characteristic function复合函数composite function映射mapping定义域domain值域range像image与……成正比be directly proportional to正变direct variation反变inverse variation性质property按推广的定义in the extended sense普遍化generalize/universalize并入incorporate无穷大infinite最大值maximum 可测空间measurable space2.9变量variable极限limit左极限left limit右极限right limit绝对值absolute value序列sequence柯西列Cauchy sequence级数series递增的increasing递减的decreasing单调的monotonic有界的bounded无界的unbounded上界upper bound最小上界least upper bound最大下界greatest lower bound有限区间finite interval无穷区间infinite interval有界集bounded set实数系real-number system趋近approach收敛converge一致收敛converge uniformly判别法criterion等价be equivalent to逐次的successive与……矛盾contradict2.10导数derivation微分differential切线tangent line即时速度instantaneous velocity差商difference quotient可视化的解释visual interpretation子区域：subdomain 逼近approximation原函数primitive function反导数antiderivative不定积分indefinite integral被积函数integrand任意常数arbitrary constant积分常数integral constant积分公式integral formula逆过程reverse process替换法积分integration by substitution分部积分integration by parts连续函数continuous function 可微函数differentiable function2.11定积分definite integral不变性invariance可加性additivity唯一性uniqueness阶梯函数step function非负函数nonnegative function放大expansion压缩contraction建立establish比较comparison成立hold严格不等式strict inequality直立柱子right cylindrical solid子区间subinterval 旋转体solid of revolution圆柱形的cylindrical单调的monotonic可测的measurable可积的integrable全等的congruent截面的cross-sectional凸的convex有效的valid2.12点状收敛converge pointwise绝对收敛converge absolutely一致收敛的uniformly convergent一致收敛converge uniformly WM判别法：weierstrass M-test比较判别法geometric series幂级数power series收敛圆circle of convergence收敛半径radius of convergence上界upper bound上有界bounded above最小上界least upper bound相邻项consecutive terms空集empty set 在内部interior to控制dominate 操作manipulate2.13方程equation齐次方程homogeneous equation齐次的homogeneous非齐次的non-homogeneous存在性existence唯一性uniqueness唯一的unique惟一地uniquely微分方程的阶order of a differential equation初始条件initial condition通解general solution特解particular solution补解complementary solution产生yield变化range输入input输出output先验的a priori2.14随机变量random variable密度函数density function方差variance偏差deviation标准差standard deviation带权平均weighted average平方根square root均方根root mean square正态分布normal distribution斯蒂尔切丝积分Stieltjes integral大数定律law of large numbers质点mass point 质心center of mass二阶矩second moment惯性矩moment of inertia旋转半径radius of gyration散步spread使散开disperse离散的discrete连续的continuous理论上theoretically2.16概率论probability theory组合分析combinatorial analysis组合学combinatorics纯数学pure mathematics数值分析numerical analysis连续数学continuous mathematics离散数学discrete mathematics有限集finite set 二项式系数binomial coefficient枚举enumeration不同的元素distinct elements逼近approximation符号运作symbolize manipulation线性插值linear interpolation无限精度infinite precision直接方法direct method 算法algorithm二分法bisection method收敛判别法convergence test牛顿法New’s method拉格朗日插值多项式Lagrange interpolation polynomial高斯消元法Gaussian elimination欧拉方法Euler’s method雅克比迭代Jacobi iteration离散化discretization连续体continuum汉译英2.7(1)Linear combination, linear dependence and linear independence are all important concepts of linear spaces.(3)Not only matrix can be used to solve a system of linear equations, but also can be used to judge whether the system of equations have solutions and whether the solution is unique.(5)This conclusion is contradictory to the hypothesis of the problem, so the proposition to be proved is true.(7)let V be an n-dimensional vector space over the field F and W be an m-dimensional vector space over the field F. Let B and B' be ordered bases for U and W respectively. Then any lineartransformation T from V into W is determined by the matrix of T relative to B and B'.2.9(1)A sequence is called monotonic if it is increasing or decreasing.(3)If a sequence {an} converges, then for any positive number c, there exists a positive integer N such that |an|<c for all n>=N.(5)Suppose the function f(x) is defined on the interval(a,infinite). If any c>0, there exists a positive integer K such that |f(x)-A|<c for all x>=K(where A is a constant), then f(x) is said to converge toA as X-+infinite. If g(x)=-f(x)converges to A as x—infinite, then f(x) is said to converge to A as x—infinite. If f(x) converges to A both as x-+infinite and as x—infinite, then f(x) is said to converge to A as x-infinite.2.10(1)People’s researches on the tangent line to a curve and instantaneous velocity of moving body leads to the generation of the concept of a derivative.(3)The tangent problem provides a visual interpretation for the derivative, which leads people to define the derivative as the limitof a difference quotient.(5)If f(x) has a first derivative f’(x) in an interval, then, it can be used to define the differential of f(x).2.11(1)The definite integral satisfies the linearity with respect to the integrand，the additivity with respect to the interval of integration and invariance under translation.(3)Step functions or other simple functions can be used to approximate integrand above and below to find the approximate value of the integral of the function discussed.(5)Let a function y=f(x) be nonnegative on the interval[a,b]. Then the solid obtained by revolving ordinate set of this function about the x-axis, is a solid of revolution, whose volume can be computed by the integral of the function ……over the interval[a,b].2.12(1)A sequence of functions which converges uniformly on an open interval(a,b) must converge at every point in the interval, but a sequence of functions which converges pointwise on an inteval(a,b) may not converge uniformly on the interval.(3)Any power series …… converge at least at the point z=0, if it converges in the entire complex plane, then its radius of convergence is positive infinite.(5)The general term of a convergent series always approaches zero, from which follows a necessary condition for a series to converge. But it is not sufficient because a series whose general term approaches zero may not converge.2.13(1)The order of a differential equation is defined as the order of the highest derivative that appears in the equation.(3)The study of existence and uniqueness of solutions ofdifferential equation is very important because the practical problems require that we answer under what conditions a differential equation in question has solutions and has a unique solution.(5)The general solution of a nonhomogeneous equation is of the following form ……，where yc（x）is the general solution of the corresponding homogeneous equation and yp（x) is a particular solution of the nonhomogeneous equation.2.14（1）The mathematical expectation E（X）and the variance Var(X)are both theoretically computable values associated with the random variable X.(3)For each random variable, a standardized random variable, whose expectation is 0 and variance is 1, can be defined(5)Laplace was the first mathematician to realize that many sequences of random variables satisfy the central limit theorem, although a few other mathematicians had known earlier that some special sequences of random variables have this property.。