数学专业英语Word文档下载推荐.docx

1、17. mathematical analysis 数学分析18. differential equation 微分方程19. higher mathematics 高等数学 higher algebra 高等代数20. equation of condition 条件等式二 句型及典型翻译1.For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions“在数学史的很长的时期内，是逻辑推理一直占据数

2、学方法的中心地位”2.An equation is a statement of the equality between two equal numbers or number symbols. equation ：“方程”“等式” 等式是关于两个数或数的符号相等的一种陈述3.In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。注 “two members”表等号

3、的两端 alike 相同的 一样的On the performance of 中的“on”引导一个介词短语做状语Eitheror4.is true “成立”5.to more and change the terms移次和变形without making the equation untrue 保持方程同解2.2几何与三角（Geometry and Trigondogy）一、词汇cube 立方体、 cylinder 柱体、 geometrical 几何的、 surface 曲面、plane 平面、 breadth 宽度、 segment 线段 弓形（面积）、abound 大量存在、 prere

4、quisite 先决条件、 sphere 球 cone 圆锥、 triangle 三角形、 solid 立体的 立体、 straight line 直线、 line segment 直线段、 infinitely 无限地、broken line 折线、 diameter 直径、 angle 角、prerequisite 先决条件、 chord 弦、 blind acceptance of 盲目接受二、典型句子翻译1. Many leading institutions of higher learning have recognized that positive benefits can b

5、e gained by all who study this branch of mathematics.其中“higher learning”表示“高学识”“博学” Positive “确实的”“肯定的”全句 许多居领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的收获。2.we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry 我们发现这些民族的土地测量者利用几何只是重新确定消

6、失了的土地标志和边界。3.A circle is a closed curve lying in one plane, all point of which are equidistant from a fined point called the center.平面上到定点的距离等于定长的所有点组成的图形叫做圆。2.3 Basic Concepts of the Theory of SetsSection A1.sets are a means by which mathematicians talk of collections of things in an abstract way 注

7、by which 引起一个定语从句 talk of “表达译为 集合是数学家们用抽象的方式来表达一些事物的集体的工具2.belong to “属于”3.even integers 偶数less than 小于more than 大于4.be denoted by 被记作5.be referred to as 被称为6.exactly the same 完全相同7.there fore , the definition requires that we call these sets equal .因此，根据定义我们认为这两个集合相等8.divisible by 被整除Section B1.Fo

8、r example, the set consisting of those positive integers less than 10. which are divisible by 4 is a subset of the set of all even integers less than.由小于10且能被4整除的正整数组成的集合是所有小于10的偶数集的子集2.“AB”读作A is contained in B or B contains A 3.A=BAB and BA A is equal to B if and only if A is contained in B，and B

9、is also contained in A4.reference to 提到 涉及 关于5.真子集 proper subset6.“” empty set 或 void set7.单元集 one element set 2.4 整数 有理数与实数（Integers, Rational Numbers and Real Numbers）一、专业词语1 rational number 有理数 irrational number 无理数2. difference 差 quotient 商3 real axis 实轴4. fraction 分数 denominator 分母 numerator 分子

10、5. 数学归纳法：proof by induction 二、Section-A Integers and rational numbers1.1+1=2The number 1 plus 1 is denoted by 22.Strictly speaking 严格地说3.repeated addition of 1 “反复加1”4.Convenient method 简便方法5.ordered field 有序域6.The sum, difference , or product of two integers is an integer ,but the quotient of two i

11、ntegers need not be an integer. （两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数）思考 What is an inductive set?A set of real numbers is called an inductive set if it has the following two properties:（a） The number 1 is in the set （b）For every x in the set , the number x+1 is also in the set.三、Section-B Geometric inte

12、rpretation of real number as points on a line1.be familiar with 熟悉 be familiar to 被某人熟悉2.If xy, the point x lies to the left of the point y“lies to ”位于如果xy, by x点位于y点的左侧3.This device for representing real numbers geometrically is a very worthwhile aid that helps us to discover and understand better

13、certain properties of real numbers这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。2.5笛卡儿几何学的基本概念（Basic Concepts of Cartesian Geometry）一、词组与词汇1. integral 积分的、整数的、积分2. calculation 计算3. the origin 坐标原点4. coordinate system 坐标系5 an ordered pair 一个有序对6. horizontal 水平的Perpendicular 垂直的7. 解析几何：analytic geometry二、Se

14、ction A-The coordinate system of Cartesian geometry 1. As mentioned earlier, one of the applications of the integral is the calculation of area.译：计算图形的面积是积分的一种重要应用。2 .If we hope to arrive at a treatment of area that will enable us to deal with many different kinds of objects, we must first find an e

15、ffective way to describe these objects. 译：如果我们希望获得面积的计算方法以便能用它来处理多种不 同类型的图形，我们就必须首先找出描述这些图形的有效办法。3 .On the x-axis a convenient point is chosen to the right of O and its distance from O is called the unit distance.在x-轴上O点右边选定一个适当的点，并把它到O点的距离称为单位长度。4.It is clear that two ordered pairs （a,b） and （c,d）

16、represent the same point if and only if we have a=c and b=d.易知当（a,b）与（c,d）表示同一点时当且仅当a=c b=dSection B Geometric figures 1. By translating these conditions into expressions, involving the coordinates x and y ,we obtain one or more equations which characterize the figure in question.“the figure in ques

17、tion”在谈论中的图形，“该图形”通过把这 些条件转化成含有坐标x和y的表达式，我们就得到了一个或多个刻画该图形特征的方程。2. Throughout their historical development, calculus and analytic geometry have been intimately intertwined.微积分与解析几何在它们的发展史上已经互相融合在一起了。3. A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and

18、 this study will be carried out in later chapters using vector methods as well as the methods of calculus.如果想拓展微积分的范围与应用，需要进一步研究解析几何，而这种研究需要用到向量的方法。2.6函数的概念与函数思想（Function concept and function idea）一、生词与词组cake 立方体 edge 棱、边 prime 素数（质数） displacement 位移 generalization 推广 domain 区域 定义域 range 值域 范围 funct

19、ion idea 函数思想 real-valued functions 实值函数 the triangle inequality 三角不等式 real variable 实变量 the identity function 恒等函数 absolute-valued function 绝对值函数 schematic representation 图解表示 二、经典句型Section A Informal description of functions1. Various fields of human have to do with relationships that exist betwee

20、n one collection of objects and another.各行各业的人们都必须处理一类事物与另一类事物之间存在的各种关系2. The force F necessary to stretch a steel spring a distance x beyond its natural length is proportional to x.把一条弹簧伸到超过其自然长度的距离x时所需要的力F与x成正比。3. That is 换句话说4. This number is said to be a function of x even though no simple algeb

21、raic formula is known for computing it （without counting）when x is known.这个数称为x的函数，尽管还没有一个简单代数式可以由已知的x计算（不通过计数求）出它的值。Section-B1. The function idea may be illustrated schematically in many ways.可以用许多方式给出函数思想的图解说明。2. The identity function 单位函数3. absolute-value function 绝对值函数作业；P48. 22.7 序列及其极限（ Sequen

22、ces and Their Limits）1.succession 连续 2.sequence 序列 数列 3.series 级数 序列 4.infinite sequence 无穷序列 5.event 事件 6.recursion formula 递推公式 plex-valued sequence 复值序列 8.real-valued sequence 实值序列 9.the positive integers=the set of all positive integers 正整数集 10.assume 假定 11.convergence 收敛 12.divergent 发散的 Conver

23、ge to 收敛于 diverge 发散 Convergent 收敛的 divergence 发散二、句型翻译1. In everyday usage of the English language, the words “sequence” and “series” are synonyms, and they are used to suggest a succession of things or events arranged in some order.在日常英语中，单词“sequence”和“series”是同义词，用以表示按某种次序排列的一串东西或事件。2. The word “

24、sequence” is employed as in the common use of the term to convey the idea of a set of things arranged in order, but the word “series” is used in a somewhat different sense.像通常用法一样，术语“sequence”用以表达按次序排列的一串东西的意思，但是“series”一词则用于某种别的意思。3. Another common way to define a sequence is by a set of instructio

25、ns which explains how to carry on after a given start.另一种常用的定义序列的方法是，通过一串指令说明在给定初项后如何给出后面一项。4.It is clear that句型2.8 函数的导数和它的几何意义The Derivative of a function and its Geomtric Interpretation一、词汇：1、derivate 导数 differentiation 微分法 The first derivate 一阶导数 The second derivate 二阶导数2. numerator 分子3. constan

26、t 常数4. interval 区间 线节 open interval close interval5. velocity 速度 Acceleration 加速度 Instantaneous 瞬时速度6. average 平均average value 平均值average rate 平均变化率7. function 函数 position function 位置函数 linear function 线性函数8. approach 趋于 逼近approach zero 09. geometric interpretation 几何解释10.respective coordinates 相应的坐

27、标11. altitude 高度12. slope 坡度 Steepness 陡峭13. tangent 正切 切线14. bound 齐 without bound=boundlessSection A The derivate of a function 1.at least 至少2.whetheror不管还是3.The quotient itself is referred to as the average rate of the change of f in the interval joining x to x+h商差表示函数f在连接x与x+h的区别上的平均变化率。4.The de

28、rivative of f at x5.formal definition 正式定义6.f prime of x7.provided=providing that8.the rate of change of f at x （f在点的变化率）9.with respect to 关于10.In general, the limit process which produces from gives us a way of obtaining a new function from a given function .11.the nth derivative of Section B: Geometric interpretation of the derivative as a slope.12.When this is interpreted geometrically it tells us that ,as gets nearer to 0, the point P remains fixed ,Q moves along the curve toward P .,and t