数学专业英语课后答案

1、数学专业英语课后答案2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理th

2、eorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadrati

3、c equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。 Math

4、ematics comes from mans social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without

5、the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。 Before 17th century, man confined himself to the elementary mathematics, i

6、. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。 Equipment is called an equation of c

7、ondition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。Equations are of very great use. We can use equations in many mathematical problems. （8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。 To solve the equation means to move and change the terms about without m

8、aking the equation untrue, until the root of the equation is obtained, which is the value of unknown term. 英译汉1.Algebra has evolved from the operations and rules of arithmetic.The study of arithmetic begins with addition,multiplication,subtraction,and division of numbers:4+7,37682,49-22,408.In algeb

9、ra we introduce symbols or letterssuch as a,b,c,d,x,y,zto denote arbitrary numbers and，instead of special cases，we often consider general statements：a+b,cd,x-y,xa.代数是从算术的运算和规则当中逐渐发展起来的，算术的研究是从数的加减乘除开始的。例如4+7，37682，49-22，408。在代数学里,我们采用符号或字母。例如a,b,c,d,x,y,z来表示任意的数字，而不考虑那些特殊情况。我们经常考虑的是一般的表达式，例如a+b,cd,x

10、-y,xa。2.The language of algebra serves a twofold purpose.First,we may use it as a shorthand to abbreviate and simplify long or complicated statements.Second,it proves a convenient means of generalizing many specific statements.代数的语言有两个作用。第一个是使用它作为一种速记法去缩减和减化那些又长又复杂的表达。第二，它被证明是一种概括许多具体的表达方式的便捷途径。3.Ma

11、ny expressions involve two or more operations.Grouping symbols tell us which operation is to be done first.The common grouping symbols are parentheses,(),brackets.,and the fraction bar,.For example,in the expression 2(3+4),we do the addition first and then we do the multiplication:2(3+4)=2(7)=14.许多数

12、学表达式包含两个或更多的运算。分组符号告诉我们哪一个运算先做。常见的分组符号是圆括号，方括号和分数线。例如，在数学表达公式2（3+4）里。我们先做加法再做乘法2（3+4）=2（7）=142.2 几何与三角词组翻译1.学会institution，建筑师 architect, 机械师 machinist, 制图员draftsman, 测量者surveyor, 木匠carpenter2.点point, 端点endpoint, 线line, 直线straight line, 线段 line segment, 曲线curved line, 折线 broken line, 射线ray , 平面 plane

13、,曲面 curved surface3.立体solid, 柱体cylinder, 立方体cube,球 sphere, 棱锥pyramid,圆锥 cone ,4.圆circle,圆心 center, 直径diameter, 半径radius, 半圆semicircle, 弦chord, 弧arc, 优弧major arc, 劣弧minor arc5.角angle, 边side, 三角形triangle, 直角三角形right triangle,斜边 hypotenuse, 直角边right-angle side6.长度length,宽度 breadth/width,厚度 thickness, 位

14、置position7.几何的geometrical,立体的 three-dimensional , 弯曲的curved,等距离的 equidistant ,无限的 infinite8.培养创造力train originality,必须的毅力 necessary perseverance , 提高鉴赏力raise/improve the appreciation ability9.消失了的边界vanishing boundaries/landmarks,有序性和优美感 orderliness and sense of beauty, 几何图形大量存在geometric forms abound

15、in , 定理成立的先决条件a prerequisite to a theorem 汉译英（1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。 Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology. （2）西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古代的数学 家对几何做了许多出色的研究。 The western experts think that geometry ha

16、d its origin in the measurements by the Babylonians and Egyptians of their lands. Infect, the ancient Chinese mathematicians made much remarkable study for geometry. （3）几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结论。 In studying geometry, the student is taught to think clearly and critically and he is led away

17、from the practice of blind acceptance of any conclusions. （4）数学培养学生的分析问题的能力，使他们能应用毅力、创造性和逻辑推理来解决问题。 Studying mathematics can develop the students ability to analyze problems and utilizing perseverance, originality, and logical reasoning in solving the problem. （5）几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关

18、。 Geometry mainly studies hot numbers but figures such as triangles, parallelograms and circles, though it is related with numbers. （6）一个立体（图形）有长、宽和高；面（曲面或平面）有长和宽，但没有厚度；线（直线 或曲线）有长度，但既没有宽度，也没有厚度；点只有位置，却没有大小。 A solid (figure) has length, width and height. A surface (curved surface or plane surface) h

19、as length and width, but no thickness. A line (straight line or curved line) has length, but no width and thickness. A point has position, but no dimension. （7）射线从某个点出发无限延伸；两条从同一点出发的射线构成了角。这两条射线称为这个 角的两边，当这两边位于同一直线上且方向相反时，所得的角是平角。 A ray starts from a point and extends infinitely far. Two rays starti

20、ng from one point form an angle, which are called two edges of the angle. When two edges lie in the same line and have opposite direction named plane angle. （8）平面上的闭曲线当其中每一点到一个固定点的距离均相等时叫做圆。这个固定点称为圆 心，经过圆心且其两个端点在圆周上的线段称为这个圆的直径，直径的一半叫做半径，这条 曲线的长度叫做周长。 A circle is a closed curve lying in one plane, al

21、l points of which are equidistant from a fixed point. The fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. Half of the diameter is called radius. The length of the circle is called circumference. 英译汉 1.In geometry

22、an angle is defined as the set of points determined by two rays land lhaving the same endpoint O. 在几何学里从同一点O出发引出的两条射线l和l所组成的点的集合叫做角。 2.In trigonometry we often interpret angles as rotations of rays.To obtain an angle we may start with a fixed ray lhaving endpoint O,and rotate it about O,in a plane,t

23、o a position specified by ray l.We call l the initial side, lthe terminal side,and O the vertex of angle. 在三角学里，我们经常解释角就是射线的旋转。在平面上，我们许会从端点是O的射线l开始让它绕着端点O旋转，转到一个位置，由射线l标注。我们把l叫做角的始边，l叫做角的终边，O叫做角的顶点。 3.A right angle is a 90angle . An angle is acute if 090or obtuse if 90180.A straight angle is a 180an

24、gle .Two acute angles are complementary if their sum is 90.Two positive angles are supplementary if their sum is 180. 直角就是一个90的角。如果090把它叫做锐角，如果900，函数 g(x)表示不超过 x 的素数的个数。 For a given real number x0, the function g(x) is defined by the number of primes less than or equal to x. （7）函数是一种对应，它未必可以表示成一个简单的

25、代数公式。 A function is a correspondence. It is not necessary to be expressed by a simple algebraic formula. （8）在函数的定义中，关于定义域和值域中的对象，没对其性质做出任何限制。 The function idea places no restriction on the nature of the objects in the domain X and in the range Y. 2.7 序列及其极限 序列及其极限 （1）序列各项对 n 的相关性常利用下标来表示，写成如下形式： a n

26、 , x n 等。 The dependence of every team of sequence on n is denoted by using subscript, and we write a n , x n and so on. （2）以正整数集为定义域的函数称为序列。 A function whose domain is the set of all positive integers is called an infinite sequence. （3）一个复值序列收敛当且仅当它的实部和虚部分别收敛。 A complex-valued sequence converges if

27、 and only if both the real part and the imaginary part converge separately. （4） 一个序列 a n 若满足： 对任意正数 ， 存在另一个正数 N （N可能与 有关） 使得 a n - L 对所有 n N 成立，就称 a n 收敛于 L。 A sequence a n is said to have a limit L if, for every positive number , there is another positive number N (which may depend on ) such that I

28、n this case, we say the sequence a n converges to L. an ? L for all n N. （5） 重要的是， 该集的每一个成员都用一个正整数标上记号。 这样一来， 就可以谈论第一项、 第二项和一般项，即第 n 项。 The important thing is that each member of the set has been labeled with an integer so that we may speak of the first term, the second term and in general, the nth

29、term. （6）若无另加申明，本章研究的序列都假定具有实的项或复的项。 Unless otherwise specified, all sequences in this chapter are assumed to have real or complex terms. （7）作为日常用语，sequence 和 series 是同义词；但作为数学术语，它们表示不同的概念。 In everyday usage of the English language, the words “sequence” and “series” are synonyms, but in mathematics

30、these words have special technical meanings. （8）术语“收敛序列”指的是具有有限极限的序列，因此，极限为无限的序列不是收敛的， 而是发散的。 The phrase “convergent sequence” is used only for a sequence whose limit is finite. A sequence with an infinite limit is said to diverge not convergence. 2.8 函数的导数和它的几何意义 （1）差商表示函数 f 在连接 x 与 x+h 的区间上的平均变化率。

31、 The different quotient is referred to as the average rate of the change of f in the interval joining x to x+h. （2）速度等于位置函数的导数。 Velocity is equal to the derivative of positing. （3）由定义导数的过程所提供的几何解释以一种自然的方式导出了关于曲线的切线思想。 The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve. （4）差商表示直线 PQ 与水平线的夹角的正切。 The difference quotient represents the trigonometric tangent of the angle that PQ makes with the horizontal. （5）在直线运动中，速度的一阶导数称为加速度。 For rectilinear motion, the fi