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theorem，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quadratic 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。
Mathematics comes from man’s 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 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. 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 condition 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 making 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 ofnumbers:4+7,37×682,49-22,40÷8.In algebra we introduce symbols or letters—such as a,b,c,d,x,y,z—to denote arbitrary numbers and，instead of special cases，we often consider general statements：a+b,cd,x-y,x÷a.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+7，37×682，49-22，40÷8。
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-y,x÷a。
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.Many expressions involve two or more operations.Grouping symbols tell us which operation is to be done first.The common grouping symbols areparentheses,(),brackets.[],and the fraction bar,—.For example,in the expression2(3+4),we do the addition first and then we do the multiplication:2(3+4)=2(7)=14.许多数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,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 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。
数学专业英语辅导资料
数学专业英语辅导资料例. Given ε> 0, there exists a positive number N such that |a n- a |<ε for all n ≥ N .译文: 对给定的ε> 0, 存在一个正数N 使得|a n- a |<ε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a >0且b <3.译文：The sufficient and necessary condition for the equality is a >0 and b <3The equality is valid when and only when a >0 and b <3.The equality is valid if and only if a >0 and b <3.The equality is valid iff a >0 and b <3.例对任意数ε > 0, 存在一个数d >0, 使得只要| x －x 0|<<="" bdsfid="77" f="" p="" 就有|="">ε . 译文: For every numberε > 0, there exists a number d >0, such that | f (x )－f (0x )| < ε whenever | x －0x | < d .例对取定的ε > 0, 存在d >0, 使得| f (x )－f (0x )| <ε 对所有满足|x －0x |<="">立. 译文: Given ε > 0, there exists d >0, such that | f (x )－f (0x )| < ε for all x with | x －0x |<="" bdsfid="86" p=""> 例2. Equations are of two kinds--- identities and equations of condition, thelatter 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 3does.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.()d ()().B h x x h a σ?=?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.22. 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 p23. “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 mathematics, physics, and engineering.例1、An equation is a statement of the equality between two equal numbers or number symbols.Equation are of two kinds---- identities and equations ofcondition. An arithmetic or an algebraic identity is an equation.等式是关于两个数或者数的符号相等的一种描述。
数学专业英语(Doc版).13
数学专业英语－Mathematical DiscoveryTo give the flavor of Polya’s thinking and writing in a very beautiful but sub tle case , a case that involve a change in the conceptual mode , I shall quote at length from his Mathematical Discovery (vol.II , pp.54 ff):EXAMPLE I take the liberty a little experiment with the reader , I shall sta te a simple but not too commonplace theorem of geometry , and then I shall t ry to reconstruct the sequence of idoas that led to its proof . I shall proceed s lowly , very slowly , revealing one clue after the other , and revealing each g radually . I think that before I have finished the whole story , the reader will seize the main idea (unless there is some special hampering circumstance ) . B ut this main idea is rather unexpected , and so the reader may experience the pleasure of a little discovery .A.If three circles having the same radius pass through a point , the circle th rough their other three points of intersection also has the same radius .Fig.1 Three circles through one point.This is the theorem that we have to prove . The statement is short and clea r , but does not show the details distinctly enough . If we draw a figure (Fig .1) and introduce suitable notation , we arrive at the following more explicit restatement :B . Three circles k , l , m have the same radius r and pass through the sa me point O . Moreover , l and m intersect in the point A , m and k in B , k and l inC . Then the circle e through A , B , C has also the radiusFig .2 too crowded .Fig .1 exhibits the four circles k , l , m , and e and their four points of in tersection A, B , C , and O . The figure apt to be unsatisfactory , however , for it is not simple , and it is still incomplete ; something seems to be missin g ; we failed to take into account something essential , it seems .We are dialing with circles . What is a circle ? A circle is determined by c enter and radius ; all its points have the same distance , measured by the leng th of the radius , from the center . We failed to introduce the common radius r , and so we failed to take into account an essential part of the hypothesis . Let us , therefore , introduce the centers , K of k , L of l , and M of m . Where should we exhibit the radius r ? there seems to be no reason to treat a ny one of the three given circles k ; l , and m or any one of the three points of intersection A , B , and C better than the others . We are prompted to connect all three centers with all the points of intersection of the respective circl e ; K with B , C , and O , and so forth .The resulting figure (Fig . 2) is disconcertingly crowded . There are so many lines , straight and circular , that we have much trouble old－fashioned maga zines . The drawing is ambiguous on purpose ; it presents a certain figure if you look t it in the usual way , but if you turn it to a certain position and lo ok at it in a certain peculiar way , suddenly another figure flashes on you , s uggesting some more or less witty comment on the first . Can you recognize i n our puzzling figure , overladen with straight and circles , a second figure th at makes sense ?We may hit in a flash on the right figure hidden in our overladen drawing , or we may recognize it gradually . We may be led to it by the effort to sol ve the proposed problem , or by some secondary , unessential circumstance . For instance , when we are about to redraw our unsatisfactory figure , we ma y observe that the whole figure is determined by its rectilinear part (Fig . 3) .This observation seems to be significant . It certainly simplifies the geometri c picture , and it possibly improves the logical situation . It leads us to restate our theorem in the following form .C . If the nine segmentsKO , KC , KB ,LC , LO , LA ,MB , MA , MO ,are all equal to r , there exists a point E such that the three segmentsEA , EB , EC ,are also equal to r .Fig . 3 It reminds you －of what ?This statement directs our attention to Fig . 3 . This figure is attractive ; it reminds us of something familiar . (Of what ?)Of course , certain quadrilaterals in Fig .3 . such as OLAM have , by hypo thesis , four equal sided , they are rhombi , A rhombus I a familiar object ; having recognized it , we can “see “the figure better . (Of what does the whole figure remind us ?)Oppositc sides of a rhombus are parallel . Insisting on this remark , we reali ze that the 9 segments of Fig . 3 . are of three kinds ; segments of the same kind , such as AL , MO , and BK , are parallel to each other . (Of what d oes the figure remind us now ?)We should not forget the conclusion that we are required to attain . Let us a ssume that the conclusion is true . Introducing into the figure the center E or the circle e , and its three radii ending in A , B , and C , we obtain (suppos edly ) still more rhombi , still more parallel segments ; see Fig . 4 . (Of wha t does the whole figure remind us now ?)Of course , Fig . 4 . is the projection of the 12 edges of a parallele piped h aving the particularity that the projection of all edges are of equal length .Fig . 4 of course !Fig . 3 . is the projection of a “nontransparent “parallelepiped ; we see o nly 3 faces , 7 vertices , and 9 edges ; 3 faces , 1 vertex , and 3 edges are invisible in this figure . Fig . 3 is just a part of Fig . 4 . but this part define s the whole figure . If the parallelepiped and the direction of projection are so chosen that the projections of the 9 edges represented in Fig . 3 are all equa l to r (as they should be , by hypothesis ) , the projections of the 3 remainin g edges must be equal to r . These 3 lines of length r are issued from the pr ojection of the 8th, the invisible vertex , and this projection E is the center o f a circle passing through the points A , B , and C , the radius of which is r .Our theorem is proved , and proved by a surprising , artistic conception of a plane figure as the projection of a solid . (The proof uses notions of solid g eometry . I hope that this is not a treat wrong , but if so it is easily redresse d . Now that we can characterize the situation of the center E so simply , it i s easy to examine the lengths EA , EB , and EC independently of any solid geometry . Yet we shall not insist on this point here .)This is very beautiful , but one wonders . Is this the “light that breaks fo rth like the morning . “the flash in which desire is fulfilled ? Or is it merel y the wisdom of the Monday morning quarterback ? Do these ideas work out in the classroom ? Followups of attempts to reduce Polya’s program to practi cal pedagogics are difficult to interpret . There is more to teaching , apparentl y , than a good idea from a master .——From Mathematical ExperienceVocabularysubtle 巧妙的，精细的clue 线索，端倪hamper 束缚，妨碍disconcert 使混乱，使狼狈ambiguous 含糊的，双关的witty 多智的，有启发的rhombi 菱形（复数）rhombus 菱形parallelepiped 平行六面体projection 射影solid geometry 立体几何pedagogics 教育学，教授法commonplace 老生常谈；平凡的。
数学专业英语(Doc版).20
数学专业英语－Sequences and SeriesSeries are a natural continuation of our study of functions. In the previous cha pter we found howto approximate our elementary functions by polynomials, with a certain error te rm. Conversely, one can define arbitrary functions by giving a series for them. We shall see how in the sections below.In practice, very few tests are used to determine convergence of series. Esse ntially, the comparision test is the most frequent. Furthermore, the most import ant series are those which converge absolutely. Thus we shall put greater emp hasis on these.Convergent SeriesSuppose that we are given a sequcnce of numbersa1,a2,a3…i.e. we are given a number a n, for each integer ｎ＞1.We form the sumsS n=a1+a2+…+a nIt would be meaningless to form an infinite suma1+a2+a3+…because we do not know how to add infinitely many numbers. However, if ou r sums S n approach a limit as n becomes large, then we say that the sum of our sequence converges, and we now define its sum to be that limit.The symbols∑a=1 ∞a nwill be called a series. We shall say that the series converges if the sums app roach a limit as n becomes large. Otherwise, we say that it does not converge, or diverges. If the seriers converges, we say that the value of the series is∑a=1∞=lim a→∞S n=lim a→∞(a1+a2+…+a n)In view of the fact that the limit of a sum is the sum of the limits, and other standard properties of limits, we get:THEOREM 1. Let{ a n}and { b n}(n=1,2,…)be two sequences and assume that the series∑a=1∞a n∑a=1∞b nconverge. Then ∑a=1∞(a n + b n ) also converges, and is equal to the sum of the two series. If c is a number, then∑a=1∞c a n=c∑a=1∞a nFinally, if s n=a1+a2+…+a n and t n=b1+b2+…+b n then∑a=1∞a n ∑a=1∞b n=lim a→∞s n t nIn particular, series can be added term by term. Of course , they cannot be multiplied term by term.We also observe that a similar theorem holds for the difference of two serie s.If a series ∑a n converges, then the numbers a n must approach 0 as n beco mes large. However, there are examples of sequences {an} for which the serie s does not converge, and yet lim a→∞a n=0Series with Positive TermsThroughout this section, we shall assume that our numbers a n are ＞0. Then t he partial sumsS n=a1+a2+…+a nare increasing, i.e.s1＜s2 ＜s3＜…＜s n＜s n+1＜…If they are approach a limit at all, they cannot become arbitrarily large. Thus i n that case there is a number B such thatS n< Bfor all n. The collection of numbers {s n} has therefore a least upper bound ,i.e. there is a smallest number S such thats n<Sfor all n. In that case , the partial sums s n approach S as a limit. In other wo rds, given any positive number ε>0, we haveS –ε< s n < Sfor all n .sufficiently large. This simply expresses the fact that S is the least o f all upper bounds for our collection of numbers s n. We express this as a theo rem.THEOREM 2. Let{a n}(n=1,2,…)be a sequence of numbers>0 and letS n=a1+a2+…+a nIf the sequence of numbers {s n} is bounded, then it approaches a limit S , wh ich is its least upper bound.Theorem 3 gives us a very useful criterion to determine when a series with po sitive terms converges:THEOREM 3. Let∑a=1∞a n and∑a=1∞b n be two series , with a n>0 for all n an d b n>0 for all n. Assume that there is a number c such thata n< cb nfor all n, and that∑a=1∞b n converges. Then ∑a=1∞a n converges, and∑a=1∞a n ≤c∑a=1∞b nPROOF. We havea1+…+a n≤cb1+…+cb n=c(b1+…+b n)≤c∑a=1∞b nThis means that c∑a=1∞b n is a bound for the partial sums a1+…+a n.The least u pper bound of these sums is therefore ≤c∑a=1∞b n, thereby proving our theore m.Differentiation and Intergration of Power Series.If we have a polynomiala0+a1x+…+a n x nwith numbers a0,a1,…,a n as coefficients, then we know how to find its derivati ve. It is a1+2a2x+…+na n x n–1. We would like to say that the derivative of a ser ies can be taken in the same way, and that the derivative converges whenever the series does.THEOREM 4. Let r be a number >0 and let ∑a n x n be a series which conv erges absolutely for ∣x∣<r. Then the series ∑na n x n-1also converges absolutel y for∣x∣<r.A similar result holds for integration, but trivially. Indeed, if we have a series ∑a=1∞a n x n which converges absolutely for ∣x∣<r, then the series∑a=1∞a n/n+1 x n+1=x∑a=1∞a n x n∕n+1has terms whose absolute value is smaller than in the original series.The preceding result can be expressed by saying that an absolutely converge nt series can be integrated and differentiated term by term and and still yields an absolutely convergent power series.It is natural to expect that iff (x)=∑a=1∞a n x n,then f is differentiable and its derivative is given by differentiating the series t erm by term. The next theorem proves this.THEOREM 5. Letf (x)=∑a=1∞a n x nbe a power series, which converges absolutely for∣x∣<r. Then f is differentia ble for ∣x∣<r, andf′(x)=∑a=1∞na n x n-1.THEOREM 6. Let f (x)=∑a=1∞a n x n be a power series, which converges abso lutely for ∣x∣<r. Then the relation∫f (x)d x=∑a=1∞a n x n+1∕n+1is valid in the interval ∣x∣<r.We omit the proofs of theorems 4,5 and 6.Vocabularysequence 序列positive term 正项series 级数alternate term 交错项approximate 逼近,近似 partial sum 部分和elementary functions 初等函数 criterion 判别准则(单数)section 章节 criteria 判别准则(多数)convergence 收敛(名词) power series 幂级数convergent 收敛(形容词) coefficient 系数absolute convergence 绝对收敛 Cauchy sequence 哥西序列diverge 发散radius of convergence 收敛半径term by term 逐项M-test M—判别法Notes1. series一词的单数和复数形式都是同一个字.例如:One can define arbitrary functions by giving a series for them(单数)The most important series are those which converge absolutely(复数)2. In view of the fact that the limit of a sum of the limits, and other standard properties of limits, we get:Theorem 1…这是叙述定理的一种方式: 即先将事实说明在前面,再引出定理. 此句用in view of the fact that 说明事实,再用we get 引出定理.3. We express this as a theorem.这是当需要证明的事实已再前面作了说明或加以证明后,欲吧已证明的事实总结成定理时,常用倒的一个句子,类似的句子还有(参看附录Ⅲ):We summarize this as the following theorem; Thus we come to the following theorem等等.4. The least upper bound of these sums is therefore ≤c∑a=1∞b n, thereby proving our theorem.最一般的定理证明格式是”给出定理…定理证明…定理证毕”,即thereby proving our theorem;或we have thus proves the theorem或This completes the proof等等作结尾(参看附录Ⅲ).5. 本课文使用较多插入语.数学上常见的插入语有:conversely; in practice; essentially; in particular; ind eed; in other words; in short; generally speaking 等等.插入语通常与句中其它成份没有语法上的关系,一般用逗号与句子隔开,用来表示说话者对句子所表达的意思的态度.插入语可以是一个词,一个短语或者一个句子.ExerciseⅠ. Translate the following exercises into Chinese:1. In exercise 1 through 4,a sequence f (n) is defined by the formula given. In each case, (ⅰ)Determine whether the sequence (the formulae are omitted).2. Assume f is a non–negative function defined for all x>1. Use the methodsuggested by the proof of the integral test to show that∑k=1n-1f(k)≤∫1n f(x)d x ≤∑k=2n f(k)Take f(x)=log x and deduce the inequalitiesc•n n•c-n< n！<c•n n+1•c-nⅡ. The proof of theorem 4 is given in English as follows(Read the proof through and try to learn how a theorem is proved, then translate this proof into Chinese ):Proof of theorem 4 Since we are interested in the absolute convergence. We may assume that a n>0 for all n. Let 0<x<r, and let c be a number such that x<c<r. Recall that lim a→∞n1/n=1.We may write n a n x n =a n(n1/n x)n. Then for all n sufficiently large, we conclude that n1/n x<c. This is because n1/n comes arbitrarily close to x and x<c. Hence for all n sufficiently large, we have na n x n<a n c n. We can then compare the series ∑nax n with∑a n c n to conclude that∑na n x n converges. Since∑na n x n-1=1n/x∑na n x n, we have proved theorem 4.Ⅲ. Recall from what you have learned in Calculus about (ⅰ) Cauchy sequence and (ⅱ) the radius of c onvergence of a power series.Now give the definitions of these two terms respectively.Ⅳ. Translate the following sentences into Chinese:1. 一旦我们能证明,幂级数∑a n z n在点z=z1收敛,则容易证明,对每一z1∣z∣<∣z1∣,级数绝对收敛;2. 因为∑a n z n在z=z1收敛,于是,由weierstrass的M—判别法可立即得到∑a n z n在点z,∣z∣<z1的绝对收敛性;3. 我们知道有限项和中各项可以重新安排而不影响和的值,但对于无穷级数,上述结论却不总是真的。
专业英语课后答案.doc
Public relations is any communication or activity intended primarily to obtain goodwill or prestige for a company through publicity.
administration costs, compliance costs, excess burden
Exe.2
货币木位
金融屮介
货帀政策T具
特许权税
电了资金转账系统
负税能力原则
公开市场业务
工资税
自动取款机
养老基金
direct finance
standard of value
standard money
The sales volume and profitability of a product will change with the elapse of time.
Exe. 4
广告是指由知名人士有偿向公众展示某种商品、服务或者创意的行为。公司广告能为公司树 立良好的形象。公益广告就有争议的社会和经济问题表明立场。产品广告主要针对某一特定 商品或服务。如果把它用于刺激对一种新产品的需求，乂可称为出导广告。比较广告也属于 产品广告，它把广告产品与竞争对手的知名产品进行比较。
intensive distribution
retail outlets
Exe. 3
Agents work on commissions based on their sales volume, and they have almost no say about policies of the company they represent.
高中数学英文试题及答案
高中数学英文试题及答案High School Mathematics English Exam Questions and AnswersQuestion 1:Solve the following quadratic equation for x:\[ 2x^2 - 7x + 3 = 0 \]Answer 1:To solve the quadratic equation \( 2x^2 - 7x + 3 = 0 \), we can use the quadratic formula:\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]where \( a = 2 \), \( b = -7 \), and \( c = 3 \). Plugging in the values, we get:\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(3)}}{2(2)} \]\[ x = \frac{7 \pm \sqrt{49 - 24}}{4} \]\[ x = \frac{7 \pm \sqrt{25}}{4} \]\[ x = \frac{7 \pm 5}{4} \]So, the solutions are \( x = 3 \) and \( x = \frac{1}{2} \).Question 2:Find the derivative of the function \( f(x) = 3x^4 - 2x^3 + x^2 + 5 \).Answer 2:To find the derivative of the function \( f(x) = 3x^4 - 2x^3 + x^2 + 5 \), we apply the power rule for derivatives:\[ f'(x) = 4 \cdot 3x^3 - 3 \cdot 2x^2 + 2 \cdot x + 0 \]\[ f'(x) = 12x^3 - 6x^2 + 2x \]Question 3:Evaluate the definite integral of the function \( g(x) = 4x - 3 \) from \( x = 1 \) to \( x = 4 \).Answer 3:To evaluate the definite integral of \( g(x) = 4x - 3 \) from \( x = 1 \) to \( x = 4 \), we integrate the function and then subtract the value of the integral at the lower limit from the value at the upper limit:\[ \int_{1}^{4} (4x - 3) \, dx = \left[ 2x^2 - 3x\right]_{1}^{4} \]\[ = (2 \cdot 4^2 - 3 \cdot 4) - (2 \cdot 1^2 - 3 \cdot 1) \] \[ = (32 - 12) - (2 - 3) \]\[ = 20 - (-1) \]\[ = 21 \]Question 4:Simplify the expression \( \frac{2x^2 - 4x + 2}{x - 1} \) by factoring.Answer 4:To simplify the expression \( \frac{2x^2 - 4x + 2}{x - 1} \), we factor out the greatest common factor from the numerator: \[ \frac{2(x^2 - 2x + 1)}{x - 1} \]Notice that the numerator is a perfect square trinomial:\[ \frac{2(x - 1)^2}{x - 1} \]Now, we can cancel out the common factor \( (x - 1) \) from the numerator and denominator:\[ 2(x - 1) \]So, the simplified expression is \( 2x - 2 \).Question 5:Determine the equation of the line that passes through the points \( (2, 3) \) and \( (-1, -2) \).Answer 5:To find the equation of the line passing through the points \( (2, 3) \) and \( (-1, -2) \), we first find the slope \( m \) of the line:\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 3}{-1 - 2} = \frac{-5}{-3} = \frac{5}{3} \]Now, using the point-slope form of a line equation \( y - y_1 = m(x - x_1) \), we can plug in one of the points and the。
专业英语课后习题答案
1. Put the following into Chinese.（1）Ohm’s law states that the voltage across a resistor is directly proportional to the current flowing through the resistor. The constant of proportionality is the resistance value of the resistor in ohms.流过电路里电阻的电流，与加在电阻两端的电压成正比，与电阻的阻值成反比。
这就是欧姆定律。
（2）Many materials, however, closely approximate an ideal linear resistor over a desired operating region.不过，许多材料在规定的工作范围内非常接近理想线性电阻。
（3）It should be noted that an ideal voltage source (dependent or independent ) will produce any current required to ensure that the terminal voltage is as stated, whereas an ideal current source will produce the necessary voltage to ensure the stated current flow.应该注意：一个理想电压源（独立或受控）可向电路提供任意电流以保证其端电压为规定值，而电流源可向电路提供任意电压以保证其规定电流。
（4）A different class of relationship occurs because of the restriction that some specific type of network element places on the variables. Still another class of relationship is one between several variable of the same type which occurs as the result of the network configuration, i. e., the manner in which the various element of the network are interconnected.一种不同类型的关系是由于网络元件的某种特定类型的连接对变量的约束。
大专数学英语考试题及答案
大专数学英语考试题及答案一、选择题（每题2分，共20分）1. 下列哪个选项是数学中的勾股定理？A. a² + b² = c²B. a² - b² = c²C. a² + c² = b²D. a² - c² = b²答案：A2. 英语中，哪个单词的意思是“图书馆”？A. LibraryB. LibraC. LabyrinthD. Labor答案：A3. 函数f(x) = 2x + 3中，当x = 1时，f(x)的值是多少？A. 5B. 4C. 3D. 2答案：A4. 英语中，哪个短语表示“在…的对面”？A. On the other side ofB. On the same side ofC. In the middle ofD. At the end of答案：A5. 以下哪个数学符号表示“不等于”？A. ≠B. =C. ≤D. ≥答案：A6. 英语中，哪个单词的意思是“计算机”？A. ComputerB. CalculatorC. CameraD. Car答案：A7. 一个圆的面积是πr²，那么半径r=2时，圆的面积是多少？A. 4πB. 2πC. πD. 8π答案：D8. 英语中，哪个短语表示“在…之后”？A. AfterB. BeforeC. DuringD. Until答案：A9. 以下哪个数学表达式表示“x的平方减去y的平方”？A. x² - y²B. x² + y²C. x - y²D. x² + y答案：A10. 英语中，哪个单词的意思是“会议”？A. MeetingB. GreetingC. EatingD. Beating答案：A二、填空题（每题3分，共30分）1. 圆的周长公式是C = _______πd，其中d是直径。
数学专业英语45753
因此，差商表示PQ与水平线的夹角a的正切。
The real number tana is called the slope of the line through P and Q and it provides a way of measuring the “steepness” of the line.
上一节描述的例子指出了介绍导数概念的方法。
We begin with a function f defined at least on some open interval (a,b) on the x-axis. 我们从一个至少定义在x轴的开区间(a,b)上的函数入 手。
Then we choose a fixed point x in this interval and introduce the difference quotient
一般地, 由f(x)产生f'(x)的极限的过程提供了一种方法, 从一个给定的函数 f 得到一个新的函数f'。这个过程 叫做微分法。 f'叫做f的一阶导数。
If f' , in turn, is defined on an open interval, we can try to compute its first derivative, denoted by f″ and called the second derivative of f.
(P67 第四段第一句话)
在直线运动中，速度的一阶导数称为加速度。
数学专业英语
MATHS ENGLISHabsolute value 绝对值 acceptable region 接受域 additivity 可加性alternative hypothesis 对立假设 analysis of covariance 协方差分析analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption checking 假设检验 availability 有效度 band 带宽bar chart 条形图 beta-distribution 贝塔分布 between groups 组间的binomial distribution 二项分布binomial test 二项检验center of gravity 重心 central tendency 中心趋势 hi-square distribution 卡方分布 chi-square test 卡方检验 classify 分类 cluster analysis 聚类分析coefficient 系数 coefficient of correlation 相关系数 collinearity 共线性 components 构成，分量 compound 复合的 confidence interval 置信区间consistency 一致性continuous variable 连续变量control charts 控制图 correlation 相关 covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点 critical value 临界值 cross tab 列联表 cubic term 三次项 cumulative distribution function 累加分布函数curve estimation 曲线估计 default 默认的 deleted residual 剔除残差density function 密度函数dependent variable 因变量design of experiment 试验设计 df.(degree of freedom) 自由度 diagnostic 诊断discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析 D-optimal design D-优化设计 effects of interaction 交互效应eigenvalue 特征值equal size 等含量estimation of parameters 参数估计 estimations 估计量 exact value 精确值 expected value 期望值 exponential指数的 exponential distribution 指数分布 extreme value 极值 factor analysis 因子分析 factor score 因子得分 factorial designs 析因设计 factorial experiment 析因试验fitted line 拟合线fitted value 拟合值fixed variable 固定变量fractional factorial design 部分析因设计 F-test F检验 full factorial design 完全析因设计 gamma distribution 伽玛分布 geometric mean 几何均值 harmonic mean 调和均值 heterogeneity 不齐性 histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性 hypothesis test 假设检验independence独立independent variable 自变量independent-samples 独立样本index of correlation 相关指数interclass correlation 组内相关 interval estimate 区间估计inverse 倒数的iterate 迭代kurtosis 峰度large sample problem 大样本问题least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level of significance 显著性水平 leverage value 中心化杠杆值 life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 lost function 损失函数 main effect 主效应matrix 矩阵 maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数 Monte Carle method 蒙特卡罗法 moving average移动平均值 multicollinearity 多元共线性 multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数 multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析 multiple regression equation 多元回归方程 multiple response 多响应 multivariate analysis 多元分析negative nonadditively 不可加性 nonlinear 非线性 nonlinear regression 非线性回归 noparametric tests 非参数检验 normal distribution 正态分布null hypothesis 零假设number of cases 个案数one-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类 optimal 优化的 optimum allocation 最优配制order statistics 次序统计量 origin 原点 orthogonal 正交的 outliers 异常值paired observations 成对观测数据paired-sample 成对样本parameter estimation 参数估计partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系 percentiles 百分位数 pie chart 饼图 point estimate 点估计poisson distribution 泊松分布 polynomial curve 多项式曲线 polynomial regression 多项式回归 polynomials 多项式 positive relationship 正相关 power 幂 P-P plot P-P概率图 predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率 probability density function 概率密度函数 quadratic 二次的 Q-Q plot Q-Q概率图 quadratic term 二次项 quality control 质量控制 quantitative 数量的，度量quartiles 四分位数 random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数 regression line 回归线rejection region 拒绝域residual 残差 residual sum of squares 剩余平方和 risk function 风险函数 robustness 稳健性 root mean square 标准差 row 行 run test 游程检验sample size 样本容量 sample space 样本空间 sampling 取样sampling inspection 抽样检验 scatter chart 散点图 S-curve S形曲线sets 集合sign test 符号检验significance level 显著性水平significance testing 显著性检验significant digits 有效数字skewed distribution 偏态分布 small sample problem 小样本问题 sort 排序sources of variation 方差来源 ion 标准离差 standard error of mean 均值的标准误差 statistical quality control 统计质量控制 std. residual 标准残差 stepwise regression analysis 逐步回归 strong assumption 强假设 stud. deleted residual 学生化剔除残差 stud. residual 学生化残差subsamples 次级样本 sufficient statistic 充分统计量 sum of squares 平方和t-distribution t分布test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验 test of independence 独立性检验 test rules 检验法则test statistics 检验统计量 testing function 检验函数 timeseries 时间序列 tolerance limits 容许限 trimmed mean 截尾均值 true value 真值 t-test t检验 two-tailed test 双侧检验unbiased estimation 无偏估计 unbiasedness 无偏性 uniform distribution 均匀分布 value of estimator 估计值variance 方差 variance components 方差分量 variance ratio 方差比weighted average 加权平均值 within groups 组内的 Z score Z分数 active constraint 活动约束 active set method 活动集法 analytic gradient 解析梯度 approximate 近似 arbitrary 强制性的 argument 变量attainment factor 达到因子 bandwidth 带宽 be equivalent to 等价于best-fit 最佳拟合 coefficient 系数 complex-value 复数值 component 分量constrained 有约束的 constraint function 约束函数 converge 收敛cubic polynomial interpolation method 三次多项式插值法 curve-fitting 曲线拟合 data-fitting 数据拟diagonal 对角的 direct search method 直接搜索法direction of search 搜索方向eigenvalue 特征值empty matrix 空矩阵exceeded 溢出的feasible solution 可行解finite-difference 有限差分 first-order 一阶 Gauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题 gradient method 梯度法 handle 句柄 Hessian matrix 海色矩阵 independent variables 独立变量inequality 不等式infeasibility 不可行性initial feasible solution 初始可行解 initialize 初始化 invoke 激活 iteration 迭代Jacobian 雅可比矩阵 Lagrange multiplier 拉格朗日乘子 large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method 列文伯格-马夸尔特法 line search 一维搜索linear equality constraints 线性等式约束 linear programming problem 线性规划问题local solution 局部解 medium-scale 中型的 mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法 multi objective 多目标的 norm 范数 observed data 测量数据optimization routine 优化过程optimizer 求解器over-determined system 超定系统 partial derivatives 偏导数polynomial interpolation method 多项式插值法quadrati二次的quadratic interpolation method 二次内插法quadratic programming 二次规划real-value 实数值 residuals 残差robust 稳健的robustness 稳健性，鲁棒性scalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method 序列二次规划法 simplex search method 单纯形法sparse matrix 稀疏矩阵 sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点 step length 步长 subspace trust region method 子空间置信域法symmetric matrix 对称矩阵termination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置unconstrained 无约束的under-determined system 负定系统weighting matrix 加权矩阵approximation 逼近a spline in b-form/b-spline b样条 a spline of polynomial piece /ppform spline 分段多项式样条bivariate spline function 二元样条函数break/breaks 断点coefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条 cubic spline interpolation 三次样条插值/三次样条内插 curve 曲线 degree of freedom 自由度 end conditions 约束条件input argument 输入参数 interpolation 插值/内插 interval 取值区间knot/knots 节点least-squares approximation 最小二乘拟合 multiplicity 重次 multivariate function 多元函数 optional argument 可选参数 output argument 输出参数point/points 数据点rational spline 有理样条rounding error 舍入误差（相对误差）sequence 数列（数组spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线 spline interpolation 样条插值/样条内插 spline surface 样条曲面 smoothing spline 平滑样条 tolerance 允许精度univariate function 一元函数 absolute error 绝对误差 absolute tolerance 绝对容限adaptive mesh 适应性网格 boundary condition 边界条件 contour plot 等值线图coordinate 坐标系decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditions 边界条件eigenvalue 特征值 elliptic 椭圆形的 error estimate 误差估计exact solution 精确解 generalized Neumann boundary condition 推广的Neumann 边界条件geometry description matrix 几何描述矩阵 geometry matrix 几何矩阵 graphical user interface（GUI）图形用户界面 hyperbolic 双曲线的 initial mesh 初始网格 jiggle 微调Lagrange multipliers 拉格朗日乘子 Laplace equation 拉普拉斯方程 linear interpolation 线性插值machine precision 机器精度mixed boundary condition 混合边界条件Neuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器normal vector 法向量Parabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变 plane stress 平面应力 Poisson's equation 泊松方程 polygon 多边形positive definite 正定refined triangular mesh 加密的三角形网格relative tolerance 相对容限 relative tolerance 相对容限 residual norm 残差范数 singular 奇异的postulate假定, 基本条件, 基本原理,要求, 假定,要求conic, conical圆锥的；圆锥形的ellipse椭圆, 椭圆形ellipt hyperbolic 双曲线的parabolic用寓言表达的: 抛物线的，像抛物线的algebraic代数的, 关于代数学的mineralogy 矿物学axiom公理collinear在同一直线上的同线的convex 凸出的；凸面的triangle三角形, 三人一组, 三角关系parallelogram平行四边形straight angle平角right angle 直角acute angle锐角obtuse angle钝角reflex angle优角rectilinear直线的；由直线组成的；循直线进行的isosceles triangle等腰三角形equilateral triangle等边三角形right triangle n. 直角三角形obtuse triangle钝角三角形acute triangle锐角三角形equiangular triangle正三角形,等角三角形hypotenuse（直角三角形的）斜边infinitesimal 无穷小的, 极小的, 无限小的calculus 微积分学, 结石inscribe 记下polygon多角形, 多边形curvilinear曲线的, 由曲线组成的intuition 直觉, 直觉的知识integral积分, 完整, 部分defective有缺陷的, (智商或行为有)欠缺的differential coefficient 微分系数irrational numbers无理数domain 定义域contradiction 矛盾continuous variable 连续变量;［连续变数］variation 变分, 变化independent variable 自变量dependent variable 应变量rectangular coordinate 直角坐标abscissa〈数〉横坐标ordinate纵线, 纵座标differential 微分的,微分(differentiation)Integral 积分, 完整, 部分(integration) trigonometry 三角法exponential 指数的, 幂数的logarithm 对数derivative导数；微商tangent 切线正切definite integral 定积分culminate 达到顶点differential equation 微分方程extreme value 极值multiple integral 多重积分functional analysis 泛函分析cardinal number 基数（如：1, 2, 3, ... 有别于序数）denumerable可数的aggregate 合计, 总计, 集合体，合计的, 集合的, 聚合的，聚集, 集合, 合计purport主旨，声称superior 长者, 高手, 上级，较高的, 上级的, 上好的, 出众的, 高傲的cumbersome 讨厌的, 麻烦的, 笨重的drastically 激烈地, 彻底地conservation 守衡律quadrature求积, 求积分interpolation插值extrapolation外推法, 推断internal point 内点generalized solution 广义解hydrodynamics 流体力学，水动力学divergence 发散（性），梯度，发散integro-interpolation method 积分插值法Variational method 变分方法comparatively 比较地, 相当地self-adjoint (nonself-adjoint) 自治的，自伴的，自共轭的finite element method 有限元法spline approximation 样条逼近Particles-in-the-Cell 网格质点法herald 使者, 传令官, 通报者, 先驱, 预兆，预报, 宣布, 传达, 欢呼advection水平对流fluctuation波动, 起伏mean-square 均方dispersion离差, 差量nterpolation 插值divisible 可分的dice, die 骰子pitfall 缺陷celestial天上的macroscopic肉眼可见的, 巨观的classical field theory 经典场理论rigit 刚硬的, 刚性的, 严格的quantum量, 额, [物] 量子, 量子论inception 起初, 获得学位pertain 适合, 属于encompass 包围, 环绕, 包含或包括某事物ingredient 成分, 因素acquainted有知识的, 知晓的 synonymous同义的configuration 构造, 结构, 配置, 外形inertia 惯性, 惯量attribute 特性momentum动量designate 指明projectile 射弹，发射的ballistics 弹道学, 发射学intractable 难处理的furnish 供应, 提供, 装备, 布置torque n. 扭矩, 转矩moment 力矩的dissipation 消散, 分散, 挥霍, 浪费, 消遣, 放荡, 狂饮constitutive构成的, 制定的continuum mechanics 连续介质力学superposition重叠, 重合, 叠合reckon 计算, 总计, 估计, 猜想，数, 计算, 估计, 依赖, 料想strength 强度load 载荷empirical 以经验为依据的insofar 在……范围cohesive 内聚性的stiffness 硬度furnish 供给turbulent 湍流laminar 层流isothermal 等温isotropic 各向同性eddy 旋涡viscosity 粘性、粘度adiabatic 绝热的reversible 可逆的 isentropic 等熵的stream tube 流管 tangential 切线的incompressible 不可压缩的similitude 相似性hydraulic 水力的,水力学的spillway (河或水坝的)放水道,泄洪道prototype 原型,样板vibratory 振动的,摆动的propagation 传播acoustic 听觉的,声学的damp 阻尼,衰减restore 复职,归还neutral 平衡 exciting force 激励力resonant共振的,谐振的stiffness 刚度,刚性magnitude 数值,大小substantially实质上的perturb 干扰,扰乱Fourier series 傅里叶级数shredder 切菜器metropolitan 大都市的at-grade 在同一水平面上elevated 高架的guide way 导轨rigid body 刚体medium 介质aging 老化polymeric聚合(物)的consolidate 把…联合为一体,统一radically 根本地,本质上deliberate 从容不迫的,深思熟虑Attribute赋予medieval 中世纪的etch 蚀刻,蚀镂fingernail 指甲bar chart 直方图joystick 游戏杆trial-error 试制, 试生产junction n. 连接, 接合, 交叉点, 汇合处contrive v. 发明, 设计, 图谋snooker (=snooker pool)彩色台球, 桌球****公理 axiom 命题 proposition 被加数augend , summand 加数addend 被减数minuend 减数subtrahend 差remainder 被乘数multiplicand, faciend 乘数multiplicator 积 product 被除数 dividend 除数 divisor 商 quotient 大于等于 is equal or greater than 小于等于 is equal or lesser than 运算符operator 算术平均数geometric mean n个数之积的n次方根（reciprocal） x的倒数为1/x 有理数 rational number 无理数irrational number 整数 integer小数点 decimal point分数 fraction 分子 numerator 分母 denominator 比 ratio 十进制 decimal system 二进制binary system 十六进制 hexadecimal system 权 weight, significance 截尾 truncation 四舍五入 round 下舍入 round down 上舍入 round up 有效数字significant digit 无效数字 insignificant digit 代数 algebra 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数 unknown, x-factor, y-factor, z-factor 等式，方程式 equation 一次方程simple equation 二次方程quadratic equation 三次方程cubic equation 四次方程 quartic equation 阶乘 factorial 对数logarithm 指数，幂 exponent 乘方 power 二次方，平方 square 三次方，立方 cube 四次方 the power of four, the fourth power n次方 the power of n, the nth power 开方 evolution, extraction 二次方根，平方根 square root 三次方根，立方根 cube root 四次方根 the root of four, the fourth root n次方根 the root of n, the nth root 坐标系coordinates 坐标轴 x-axis, y-axis, z-axis 横坐标 x-coordinate 纵坐标y-coordinate 原点origin 象限quadrant 截距(有正负之分)intercede （方程的）解solution 线段 segment 射线 radial 平行parallel 相交intersect 角度degree 弧度radian 钝角obtuse angle 平角 straight angle 周角 perigon 底 base 锐角三角形 acute triangle 直角边 leg 斜边 hypotenuse 勾股定理 Pythagorean theorem 钝角三角形 obtuse triangle 不等边三角形 scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogram 周长perimeter 全等congruent 三角 trigonometry 正弦 sine 余弦 cosine 正切 tangent 余切 cotangent 正割 secant 余割 cosecant 反正弦 arc sine 反余弦 arc cosine 反正切 arc tangent 反余切 arc cotangent 反正割arc secant 反余割 arc cosecant 集合aggregate 空集 void 子集subset 交集intersection 并集union 补集complement 映射mapping 定义域 domain, field of definition 值域 range 单调性monotonicity 图象 image 数列，级数 series 导数 derivative 无穷小infinitesimal 复数complex number 矩阵matrix 行列式determinant 半圆 semicircle 扇形 sector 环 ring 椭圆 ellipse 圆周 circumference 轨迹 locus, loca(pl.) 平行六面体 parallelepiped 立方体 cube 七面体 heptahedron 八面体 octahedron 九面体 enneahedron 十面体 decahedron 十一面体 hendecahedron 十二面体 dodecahedron 二十面体 icosahedron 多面体 polyhedron 四面体 tetrahedron 五面体pentahedron 六面体hexahedron 菱形rhomb, rhombus, rhombi(pl.), diamond 正方形 square 梯形 trapezoid 直角梯形 right trapezoid 等腰梯形 isosceles trapezoid 五边形 pentagon 六边形 hexagon 七边形heptagon 八边形 octagon 九边形 enneagon 十边形 decagon 十一边形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon 相位 phase 振幅 amplitude 内心 incentre(BrE), incenter(AmE) 外心 excentre(BrE), excenter(AmE) 旁心 escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆 inscribed circle 外切圆circumcircle 方差variance 标准差root-mean-square deviation, standard deviation 百分点 percentage 百分位数 percentile 排列permutation 分布 distribution 正态分布 normal distribution 非正态分布abnormal distribution 条形统计图bar graph 柱形统计图histogram 折线统计图 broken line graph 曲线统计图 curve diagram 扇形统计图pie diagram**** mutually disjoint events 互不相交事件mutually disjoint subsets 互不相交子集 mutually independent events 互相独立事件myria 万 myriad 无数的 multiplicity 重数 mid square method 平方取中法 midperpendicular 中垂线 minor 子式 minor arc 劣弧 mixed number 带分数 regular convergence 正则收敛 relative discriminant 相对判别式relative error 相对误差 relative extremum 局部极值 ricci equatoin 李奇恒等式ricci identity 李奇恒等式riemann function 黎曼函数riemann integral 黎曼积分 right direct product 右直积 right endpoint 右端点 right inner product 右内积 ring of integers 整数环 ring of matrices 矩阵环 root mean square error 均方根差 root of equation 方程式的根 rotation of axes 坐标轴的旋转 rotation of co ordinate system 坐标轴的旋转 round off error 舍入规则 round up error 舍入规则 runge kutta method 龙格库塔法 n disk n维圆盘 nth member 第n项 nth partial quotient 第n偏商 nth power operation n次幂运算 nth root n次根 nth term 第n项 n times continuously differentiable n次连续可微的natural injection 自然单射natural isomorphism 自然等necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量 neutral element 零元素 neutral line 中线 nonhomogeneous linear boundary value problem 非齐次线性边值问题 nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分方程组interval algebra 区间代数 interval analysis 区间分析 interval closed at the right 右闭区间 interval estimation 区域估计 intervalfunction 区间函数 interval graph 区间图 interval of convergence 收敛区间 interval of definition 定义区间 interval topology 区间拓扑irreducible set 不可约集 irreducible r module 不可约r模 periodical decimal fraction 循环十进小数 pentad 拼五小组 pentadecagon 十五边形pentagon 五角形 pentagonal number 五角数 pentagonal pyramid 五角锥pentagram 五角星 pentahedron 五面体 pentaspherical coordinates 五球坐标 penalty method 补偿法 pascal distribution 帕斯卡分布 partition function 分折函数 partial differential equation of elliptic type 椭圆型偏微分方程 partial differential equation of first order 一阶偏微分方程 partial differential equation of hyperbolic type 双曲型偏微分方程 partial differential equation of mixed type 混合型偏微分方程partial differential equation of parabolic type 抛物型偏微分方程partial differential operator 偏微分算子parametric test 参数检验particular solution 特解parallelogram axiom 平行四边形公理orthogonality relation 正交关系 ordinary differential equation 常微分方程optimal value function 最优值函数opposite angles 对角opposite category 对偶范畴 one to one mapping 一一映射 onto mapping 满射 open mapping theorem 开映射定理 one to many mapping 一对多映射one sided limit 单侧极限 numerical solution of linear equations 线性方程组的数值解法 null set 空集 null solution 零解 third boundary condition 第三边界条件two sided neighborhood 双侧邻域unbiased estimating equation 无偏估计方程unbounded function 无界函数unbounded quantifier 无界量词uncertainty principle 测不准原理uncorrelated random variables 不相关随机变量 undetermined coefficient 末定系数 velocity distribution 速度分布 velocity optimal 速度最优的weak approximation theorem 弱逼近定理 weak completeness 弱完备性weak continuity 弱连续性 weak convergence 弱收敛 wiener measure 维纳测度word group 自由群 sample correlation coefficient 样本相关系数sample covariance 样本协方差schwarz inequality 施瓦尔兹不等式second boundary condition 诺伊曼边界条件second comparison test 第二比较检验second limit theorem 第二极限定理 self adjoint differential equation 自伴微分方程 semimajor axis 半长轴semiminor axis 半短轴 sentential calculus 命题演算 set of measure zero 零测度集 set topology 集论拓扑simple connectedness 单连通性slope function 斜率函数 solution curve 积分曲线 solution domain 解域solution set of equation 方程的解集spatial co ordinate 空间坐标specific address 绝对地址spherical bessel function 球贝塞耳函数 spherical cap 球冠 spherical coordinates 球极坐标 spherical curvature 球面曲率 spherical shell 球壳 spherical zone 球带spline function 样条函数spline interpolation 样条内插stability conditions 稳定条件 statistical hypothesis testing 统计假设检验strict inequality 严格不等式strict isotonicity 严格保序性strict isotony 严格保序性strict increasing 严格递增system of partial differential equations 偏微分方程组system of ordinary differential equations 常微分方程组system of linear homogeneousequations 线性齐次方程组 system of linear inhomogeneous equations 线性非齐次方程组system of inequalities 联立不等式system of polarcoordinates 极坐标系system of variational equations 变分方程组system with concentrated parameters 集中参数系统system with distributedparameters 分布参数系统 t1topological space t1拓扑空间 t2topologicalspace t2拓扑空间 t3topological space 分离空间 t4topological space 正则拓扑空间 t5 topological space 正规空间 t6topological space 遗传正规空间 tangent cone 切线锥面 telegraph equation 电报方程 theorem for damping 阻尼定理****充分条件sufficient condition必要条件necessary condition 充要条件sufficient and necessary condition……的充要条件是……… if and only if …****abscissa 横坐标 alternatingseries 交错级数 angle of the sector 扇形角 arbitrary constant 任意常数 augmented matrix 增广矩阵 axis of parabola 拋物线的轴 axis of revolution 旋转轴 axis of rotation 旋转轴 binomial series 二项级数binomial theorem 二项式定理 binomial distribution 二项分布 bisectionmethod 分半法；分半方法 bounded above 有上界的；上有界的 boundedbelow 有下界的；下有界的bounded function 有界函数boundedsequence 有界序列brace 大括号bracket 括号Cartesian coordinates 笛卡儿坐标 certain event 必然事件 circumcentre 外心；外接圆心 circumcircle 外接圆 classical theory of probability 古典概率论 cofactor 余因子; 余因式 common denominator 同分母；公分母 commondifference 公差 common divisor 公约数；公约 common logarithm 常用对数 common multiple 公位数；公倍 common ratio 公比 commutative law 交换律 compasses 圆规 Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式central limit theorem 中心极限定理 centripedal acceleration 向心加速度concave downward 凹向下的concurrent 共点concyclic 共圆concyclic points 共圆点Euclidean geometry 欧几里德几何Euler'sformula 尤拉公式；欧拉公式 even function 偶函数 even number 偶数（2）博奕 Gaussian distribution 高斯分布 greatest term 最game （1）对策；大项 greatest value 最大值 harmonic mean (1) 调和平均数; (2) 调和中项 harmonic progression 调和级数 higher order derivative 高阶导数improper fraction 假分数improper integral 广义积分; 非正常积分implicit function 隐函数 incircle 内切圆 inclined plane 斜 included angle 夹角 indefinite integral 不定积分 initial condition 原始条件；初值条件 initial-value problem 初值问题 interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角isosceles triangle 等腰三角形 iterate (1)迭代值; (2)迭代 Lagrange interpolating polynomial 拉格朗日插值多项代Laplace expansion 拉普拉斯展式 lemniscate 双纽线 left hand limit 左方极限 limiting case 极限情况limiting position 极限位置line of best-fit 最佳拟合line segment 线段 logarithmic equation 对数方程 mathematical analysis 数学分析mathematical induction 数学归纳法monotonic decreasing function 单调递减函数 monotonic convergence 单调收敛性 monotonic increasing function 单调递增函数multiple-angle formula 倍角公式multiple root 多重根 mutually disjoint 互不相交 mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直 numerical method 计算方法；数值法oblique cone 斜圆锥 orthogonal circles 正交圆 orthogonality 正交性oscillatory convergence 振动收敛性 ordinary differential equation 常微分方程pairwise mutually exclusive events 两两互斥事件place holder 补位数字 point of inflection (inflexion) 拐点; 转折点Pisson distribution 泊松分布point-slope form 点斜式polar coordinate plane 极坐标平面polynomial equation 多项式方程posterior probability 后验概率; 事后概率premultiply 前乘; 自左乘prime factor 质因子；质因素 prime number 素数；质数 principal angle 主角principal axis 主轴 principal value 主值 prior probability 先验概率; 事先概率 probability density function 概率密度函数 product and sum formula 和积互变公式 product sample space 积样本空间 product to sum formula 积化和差公式 proof by contradiction 反证法; 归谬法 proper fraction 真分数proper integral 正常积分proper subset 真子集propositional calculus 命题演算propositional inference 命题推演protractor 量角器Pythagoras' theorem 勾股定理Pythagorean triplet 毕氏三元数组 quadratic convergence 二阶收敛性 quadrature 求积法 quotient set 商集 radial component 沿径分量 radical axis 根轴range 值域；区域；范围；极差；分布域 rationalization 有理化 raw data 原始数据 rectifiable 可求长的 reciprocal 倒数 rectangular coordinate plane 直角坐标平面 recurrence formula 递推公式 reducibility 可约性; 可化简性 reflexive relation 自反关系 reference angle 参考 reference line 基准线 reflex angle 优角；反角 region of acceptance 接受区域region of convergency 收敛区域 region of rejection 否定区域 right circular cone 直立圆锥（体） resolution of vector 向量分解; 矢量分解right hand limit 右方极限 right prism 直立棱柱；直立角柱(体) right pyramid 直立棱锥；直立角锥(体) right-angled triangle 直角二角形scalene triangle 不等边三角形；不规则三角形 scatter diagram 散点图scientific notation 科学记数法semi-conjugate axis 半共轭轴semi-transverse axis 半贯轴semi-vertical angle 半顶角separable differential equation 可分微分方程septic equation 七次方程set square 三角尺；三角板 shaded portion 有阴影部分 significance level 显著性水平 significant figure 有效数字 similar triangles 相似三角形simple iteration method 简单迭代法simple pendulum 单摆Simpson's integral 森逊积分 standard deviation 标准差；标准偏离 standard normal distribution 标准正态分布; 标准常态分布 stationary point 平稳点; 逗留点; 驻点 strictly monotonic 严格单调 statistical chart 统计分析submultiple angle formula 半角公式subsidiary angle 辅助角substitution 代入; 代入法successive approximation 逐次逼近法successive derivative 逐次导数 successive differentiation 逐次微分法suffix 下标 sum to infinity 无限项之和 sum to product formula 和化积公式 superimposing 迭合 supplementary angle 补角 surjection 满射symmetric relation 对称关系 tautology 恒真命题；恒真式 Taylor’s expansion 泰勒展开式 Taylor’s series 泰勒级数 Taylor’s theorem 泰勒定理 test criterion 检验标准 test of significance 显著性检验 to the nearest 至最接近之torque 转矩torus 环面transcendental function 超越函数 transformation of variable 变数转换 transitive 可传递的 transpose of matrix 倒置矩阵；转置矩阵 transversal 截 ；横截的 triangle law of addition 三角形加法 travel graph 行程图 tree diagram 树形图trapezoidal integral 梯形积分truncated Taylor’s series 截断泰勒级数 two-tailed test 双尾检验；只端检验 type I error I 型误差type II error II型误差unbiased estimator 无偏估计量undetermined coefficient 待定系数 unique solution 唯一解 vertical asymptote 垂直渐近线 vertically opposite angles 对顶角 without loss of generality 不失一般性****分子Numerator 分母Denominator 阿拉伯数字Hindu-Arabic numeral假分数Improper fraction 最大公因子Highest Common Factor (H.C.F.) 最小公倍数 Lowest Common Multiple (L.C.M.) 行列式 determinant****interval closed at the right 右闭区间 interval of convergence 收敛区间interval of definition 定义区间invariance theorem 不变性定理 invariant of an equation 方程的不变量 inverse circular function 反三角函数 inverse hyperbolic function 反双曲函数inversion formula 反演公式 isotonic injective mapping 保序单射映射jacobi identity 雅可比恒等式 jump point 跳跃点 law of double negation 双重否定律 law of inertia 惯性律law of large numbers 大数定律 leading ideal 猪想 liouville theorem 刘维尔定理 lipschitz condition 李普希茨条件 markov transform 马尔可夫变换 mathematical approximation 数学近似法 mathematical model 数学模型 maximum condition 极大条件 maximum deviation 最大偏差 mean square deviation 方差 mean square of error 误差的均方 meromorphic function 亚纯函数柱形统计图 histogram 折线统计图 broken line graph 曲线统计图 curve diagram 扇形统计图 pie diagram排列 permutatio内切圆 inscribed circle 外切圆 circumcircle正多边形 equilateral polygon metric space 度量空间 metric subspace 度量子空间method of runge kutta type 朗格库塔型的方法 method of steepest ascent 最速上升法 method of steepest descent 最速下降法method of finite elements 有限元法method of fractional steps 分步法method of exhaustion 穷竭法 method of approximation 近似法 method of artificial variables 人工变量法method of balayage 扫除法method of characteristic curves 特者法 method of comparison 比较法 method of conjugate gradients 共轭梯度法lateral area 侧面积 last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计method of difference 差分法method of elimination 消元法method of estimation 估计法meromorphic differential 亚纯微分 median 中位数 measuring rule 量尺 mean term 内项mean term 内项mean term 内项irreducibility criterion 不可约性判别准则irreducible polynomial 不可约多项式 irreducible generating set 不可约生成集 irregular divisor class 非正则因子类 irregular point 非正则点irregular singular point 非正则奇点isometric circle 等距圆isometric embedding 等距嵌入isomorphic field 同构域isomorphic graph 同构图isomorphic group 同构群isomorphic image 同构象isothermal parameter 等温参数iterated function 叠函数iterated integral 累积分joint distribution 联合分布 jordan algebra 约当代数kernel of an integral equation 积分方程的核l'hospital rule 洛必达规则laboratory system of coordinates 实验室坐标系 labyrinth 迷宫lacation principle 介值定理lag correlation coefficient 滞后相关系数lag regression 落后回归laguerre differential equation 拉盖尔微分方程lame equation 拉梅方程language of formula 公式语言 laplace beltrami operator 拉普拉斯贝尔特拉米算子lateral area 侧面积 last multiplier 最后乘子large sample test 大样本检验lattice constant 点阵常数lattice design 格子设计 left adjoint 左伴随的 left derivative 左导数left differential 左微分 left direct product 左直积 left end point 左端点 left length 左长 left limit value 左极限值left multiplication ring 左乘环length of curve 曲线的长 length of normal 法线的长 levi decomposition 列维分解 limes inferior 下极限 limes superior 上极限limit circle 极限圆 limit circle type 极限圆型logarithm to the base 10 常用对数logarithmic normal distribution 对数正态分布logic of relations 关系逻辑magic circle 幻圆magic cube 幻立方manifold without boundary 无边廖many valued mapping 多值映射marginal distribution density function 边缘分布密度函数 marginal distribution function 边缘分布函数mathematical programming 数学规划 mathematical random sample 数学随机样本 mathematical statistics 数理统计 maximum likelihood estimating function 极大似然估计量 independent variable 自变量 dependent variable 应变量equiangular triangle 正三角形,等角三角形命题proposition 差remainder 积product 除数divisor 商quotient 截尾truncation 未知数unknown, x-factor, y-factor, z-factor 阶乘 factorial 集合 aggregate 空集 void 子集 subset 交集 intersection 并集 union 补集 complement 映射 mapping 勾股定理 Pythagorean theorem 菱形 rhomb, rhombus, rhombi(pl.), diamond 双曲线 hyperbola 抛物线 parabola topology of bounded convergence 有界收敛拓扑toroid 超环面 toroidal coordinates 圆环坐标trace of dyadic 并向量的迹transcendental integral function 超越整函数transformation formulas of the coordinates 坐标的变换公式 transformation to principal axes 轴变换 transversal lines 截线trapezoid method 梯形公式trefoil knot 三叶形纽结truth function 真值函项two sided test 双侧检定 two sided neighborhood 双侧邻域two sided surface 双侧曲面two termed expression 二项式ultrahyperbolic equation 超双曲型方程。
专业英语课后题答案.doc
Unit 1 The Fundamentals of Computers1.1The Varieties of Computers•IIL Translating.- 1. Original: Primary storage, or memory, is the internal computer circuitry that temporarily holds data waiting to be processed. Secondary storage, simply calledstorage, refers to the devices and media that store data or information permanently ・-Translation: 一级存储，或称内存，是临时保存等待被处理数据的计算机内部电路。
而二级存储，简称存储器，是指那些永久性存储数据或信息的设备和介质。
一2. Original: A biological nanocomputer, which would be made of DNA and could fit into a single human cell, would use DNA as its software and enzymes as its hardware;its molecular-sized circuits would be viewable only through a microscope.-Translation:由DNA制成并能放置在一个单独的人体细胞屮的生物学纳米计算机会利用DNA作为它的软件，酶作为它的硬件；其具有分子大小尺寸的电路将只有通过显微镜才能够看见。
1.2The History of Computers•III. Translating・- 1. Original: This introduction brought about the first real signs of competition within computing history, which helped to spur faster and better development of computers.-Translation:这一引入带来了计算历史屮可谓第一个真正的竞争标志，有助于刺激计算机更快-更好的发展。