数学专业英语课后答案
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。
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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。