数学与应用数学专业英语期末考试试题

一、英文表示： 1.13.25 thirteen-point-two-five 2.a n b

=log the logarithm of n to the base b equals a 3.5/8 five eighths 4.

3152a -+x the fifth root of a squared plus x to the minus one third 5.0x

5232=--a x to the minus two thirds plus the fifth root of a squared equals zero 6.))((a 2233b ab a b a b +-+=+ a cubed plus b cubed equals a plus b into a squared minus ab plus b squared

二、英语名词定义

1.Equation

An equation is a statement of the equality between two equal number symbols. 2.Function

The modern definition of a function y of x is simply a mapping from a space X to another space Y.A mapping defined when every point x of X has a definite image y, a point of Y. 3.The limit of a sequence {}f(n)(for example L n f =∞

→)(lim n ) : A sequence {}f(n) is said to have a limit L if ,for every positive number ε,there is another positive number N (which may depend on ε)such that

ε<-L n f )( for all n>=N In this case, we say the sequence {}f(n) converges to L and we write

L n f =∞→)(lim n ,or L n f →)( as ∞→n .A sequence which does not converge is called divergent.

4.The derivative of function f(x)

The derivative )x (‘f is defined by the equation h

x f h x f f h )()(lim )x (0-+=→‘ provided the limit exists. The number )x (‘f is also called the rate of change of f at x.

5.Statistical population A statistical population is the set of measurements (or record of some qualitative trait)corresponding to the entire collection of units about which information is sought.

三 几何图形的名称

1.圆 Circle

2.椭圆 ellipse

3.长方形 rectangle

4.正方形 square

5.平行四边形 parallelogram

6.三角形 triangle

7.立方体 cube

8.圆锥 cone

9.曲线 curve 10.双曲线 hyperbola

四．英译汉

1.This device for representing real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers. However, the readers should realize that all properties of real numbers that are to be accepted as theorems must be deducible from the axioms without any reference to geometry. This does not mean that one should not make use of geometry in studying properties of real numbers. On the contrary ,the geometry often suggests the method of proof of particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof(one depending entirely on the axioms for the real numbers).In this book, geometric arguments are used to large to help motivate or clarify a particular discuss. 译文：几何化地表示实数的方法是一种非常有益的辅助手段，它可以帮助我们发现和更好的了解实数的某些性质。然而，读者应该意识到，那些将要被采用作为定理的所有有关实数的性质时不应该使用几何学。相反地，几何学经常启发特殊定理的证明方法，而且，有时候，几何学方面的论点比纯分析（它完全依赖与实数的公理）的证明更直观。在本书中，几何学的论点会大范围地使用，以帮助人们推动或阐明一些特殊的讨论。