数学专业英语辅导资料.docVIP

例. Given 0, there exists a positive number N such that |ana| for all n ≥ N . 译文: 对给定的 0, 存在一个正数N 使得|ana|对所有的 n ≥ N 都成立. 例2. Since h(x) is harmonic on a neighborhood of B(a, r), we have 译文: 因为h(x)在某个邻域B(a, r)内调和, 故 例 该等式成立的充分必要条件是a0且b3. 译文：The sufficient and necessary condition for the equality is a0 and b3 The equality is valid when and only when a0 and b3. The equality is valid if and only if a0 and b3. The equality is valid iff a0 and b3. 例 对任意数 0, 存在一个数d 0, 使得只要| x－x0|d 就有| f (x)－f ()| . 译文: Fornumber 0, there exists a number d 0, such that | f (x)－f ()| whenever | x－| d . 例 对取定的 0, 存在d 0, 使得| f (x)－f ()| 对所有满足|x－|d 的x都成立. 译文: Given 0, there exists d 0, such that | f (x) －f ()| for all x with | x－|d . 例2. Equations are of two kinds--- identities and equations of condition, the latter is called equations for short 等式分为两类，恒等式和条件等式，后者简称为方程. 例3. An arithmetic or an algebraic identity is an equation. 译文: 代数和算数的恒等式都是等式. 例4. After checking , we see －3 does not satisfy the original equation, but 3 does. 译文：经检验得知, －3不满足原方程,但是3却是方程的根. 例5. The square root of a negative number is a pure imaginary . 译文：负数的平方根是纯虚数. 例. The values of the constructed function should not exceed the maximum permissible. 译文：构造的函数的值不应超过所允许的最大数值. 例11. We call a triangle an obtuse triangle when one angle is an obtuse angle. 译文：有一个角为钝角的三角形被称为钝角三角形. 例12. A great deal of practical problems can be solved with the differential equations. 译文：使用微分方程, (人们)可以解决大量的实际问题. . The most famous quantity in mathematics is the ratio of the circumference of a circle to its diameter, which is also known as the number pi and denoted by the Greek letter p 23. “Linear algebra” is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathemat