数学专业英语 第2章课后答案Word文件下载.docx

1、angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:

2、be denoted as 定义为:be defined as3.（1）Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.（3）If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by usin

3、g the law of cosines.（5）Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.（1）如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向,这个角被称为处于标准位置.（3）仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观

4、测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.（5）如果我们知道一个三角形的两条边的长度和对着其一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest comm

5、on divisor（G.C.D） 最小公倍数: lowest common multiple（L.C.M） 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.（1）We need to study by which integers an integer is divisible, tha

6、t is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.（3）The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.（5）Th

7、e number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.（1）数论一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.（3）一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.（5）任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么（p,m）=1.2.42.集:se

8、t 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.（1）Set theory has become one of the common

9、 theoretical foundation and the important tools in many branches of mathematics.（3）Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.（5）The subset T of set S can often be denoted by x, that is, T consists of those elements x for whic

10、h P（x） holds.（7）This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.（1）设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N的补集是所有奇数的集合.（3）一个非空集合S称为由上界的,如果存在一个数c具有属性:x=1,这个n元数组称为一个n维点或者一个n维向量,各个数a1,a2,an称为这个向量的坐标或者分量。（3）向量x1,x2,xn称为线性相关的,

11、如果存在不全为0的标量使得a1x1+a2x2+anxn=0.向量x1,x2xn称为线性无关的,如果x1,x2xn不是线性相关的。2.72.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:scalarproduct 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:z

12、ero 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:mathematical economics 量子力学:quantum mechanics 相容的:consistent 最终的:ultimately3.（1）Linear combination, linear dependence and linear independenceare all important concepts of linear spaces.（3）N

13、ot 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

14、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 beordered 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.4.（1）如果V和W是在域F上的向量空间,任何V到W的到上的一一对应的线性变化T称为一

15、个V到W到上的同构。如果存在一个V到W到上的同构,我们说V同构于W。（3）当p=1,一个p*q的矩阵只有一行,称为一个行向量。当q=1时,该矩阵只有一列,称为一个列向量。当p和q都是1时,这种情况相当不值一提,这里不需要关注. 一个有p个元素的列向量我们成为一个p向量,所以一个p向量是一个p*1的矩阵。（5）一个m*n的矩阵有m个行向量和n列向量。设A是一个有实数元素的n阶方阵,那么A的n个行向量是线性无关的当且仅当行列式|A|不等于0.进一步, A的n个列向量是线性相关的当且仅当A的n个列向量是线性相关的。332.8函数关系:function relation 表格:table 反函数:in

16、verse 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

17、 最大值:maximum 可测空间:measurable space3.（1）Because the concept of function originated in physics, in the seventeenth century, people once believed that the function relation was nothing but a formula.（3）If to each value of the variable x, the variable y has adefinite value corresponding,then the variabl

18、e y is the function of variable x.（5）If f is a mapping from a space X to another space Y and g is a mapping from the space Y to the another space Z, then we can define a composite mapping h=g.f, which is a mapping from X to Z.4.（1）函数提供了一个研究一些变量的方法,所研究的变量随着其他的量变化,也就是说,当一个量的变化引起了另一个量相应的变化时。（3）对一个函数f:D

19、-R.我们定义f（D）=y in R|y=f（x） x属于D,并f（D）是f的像。我们说f:D-R达到一个最大值,如果使像f（D）有一个最大值,即有一个点x0属于D使得f（x）=f（x0）.（5）要画出一个新的函数y=f（x）,即一个我们不熟悉的函数图象,我们可以按以下方式使用一些作图建议。（a）确定函数的定义域。（b）确定此方程拥有的任何类型的对称性。如果f（x）=f（-x）,那么函数表现出y 轴轴对称性。如果f（-x）=-f（x）,那么函数表现出原点对称性。（c通过x=0处对f（x）取值求y截距,通过求x的值使f（x）=0求x截距。（d）建立一个满足方程y=f（x）的有序对的表格。（e）描

20、画出于有序对有关的点,并用一条平滑的曲线连接它们,然后,如果合适,则根据图像所拥有的任何对称性反射出曲线的这一部分。2.92.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 l

21、ower 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: contradict3.（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|=N.（5）Suppose the function f（x） is defined on the interval（a,infinite）. If any c0, there exists a positive integer K such that |f（x）-A|=K（where A is a constant）, then f（x） is said to converge to A