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1、Part I FUNDAMENTALS,Unit 1-Text(1),Words&ExpressionsAlgebra 5AldVibrEn.代数学algorithm 5AlEriTEmn.算法arithmeticE5riWmEtikn.算术calculus 5kAlkjulEsn.微积分curriculumkE5rikjulEmn.课程differentiation7difE7renFi5eiFEnn.微分discipline 5disiplinn.学科discrete dis5kri:tadj.离散的equation i5kweiFEnn.方程式；等式evaluationi7vAlju5e
2、iFEnn.赋值；值的计算exponential7ekspEu5nenFEladj.指数的，幂数的formalism5fC:mElizEmn.形式heterogeneity7hetErEudVi5ni:itin.异种，异质，不同成分integration7inti5reiFEnn.积分,limit5limitn.极限linear5liniEadj.线性的（nonlinear，非线性的）logarithmic7lCE5riWmikadj.对数的matrix5meitriksn.矩阵oscillatory5CsileitEriadj.振荡的；变动的sequence 5si:kwEnsn.序列sta
3、tistics stE5tistiksn.统计；统计学trigonometrictrIEnE5metrIkadj.三角学的；三角法的variable 5vZEriEbln.变量 vector5vektEn.矢量，向量Expert system专家系统Fourier series傅里叶级数Oral presentation 口头报告Ordinary Differential Equation常微分方程(abbr.ODE),Unit 1-Text(2),Notes1 Developments in computer technology and related software have prov
4、ided theengineer with tools of increasing power and sophistication which have significantimplications for the use and role of mathematics in engineering practice.,Unit 1-Text(3),本句中which引导的定语从句修饰整个主句，have implication for表示“暗示”。,计算机技术及其相关软件的发展为工程技术人员提供了功能强大且日趋完善的工具，使数学应用于工程实践并发挥着重要作用。,Notes2 If engin
5、eers are to take full advantage of sophisticatedcompu-tational tools then it is essential that they become effective at mathematicalmodelling and discriminating,intelligent and wary users of packaged software andother aids to computa-tional modelling.,Unit 1-Text(4),由that引导的主语从句（it是形式主语）中become做谓语，后
6、接两个并列成分effective at和users of，其中discriminating,intelligent及wary均修饰users。,如想充分利用这些复杂的计算工具，工程技术人员必须熟悉数学建模，能区别各种软件包及其他计算建模辅助工具，并能灵活运用。,Notes3There is little doubt that a high degree of fluency in the manipulation of mathematical expressions will always be required,forwithout this there can be no real un
7、derstanding.,Unit 1-Text(5),本句中for表示原因，manipulation原义为“操纵、控制”，这里转译为“运用”。,毫无疑问，学生必须熟练运用数学公式，否则就不可能有真正意义上的理解。,Notes4 Consequently,this book is not a collection of recipes and techni-ques designed toteach students to solve routine exercises,nor is mathematical rigour introducedfor its own sake.,Unit 1-
8、Text(6),本句中not(neither)nor，表示“既不也不”，for ones own sake作“为了它自己的好处”解。,因此，本书既不是教授学生解题方法与技巧的汇总，也未以数学本身所要求的严谨方式编写。,Notes5 As a result of the widening of access opportunities,particularly in the UnitedKingdom,there is increasing heterogeneity in background knowledge in mathematicsof students entering degre
9、e courses in engineering.,Unit 1-Text(7),本句中access 原意“通路，访问，入门”，heterogeneity原意“异种，异质，不同成分”，翻译时难度较大，需要在充分理解的基础上意译。,由于入学机会增多，修读工程类学位课程学生的数学基础愈见参差不齐，尤以英国为甚。,科技文章 文体特点：语言简练、结构严谨、逻辑性强、原理概念清楚、重点突出、段落章节分明。,Unit 1-Grammer(1),科技英语 传递信息的工具 客观外部世界的本质和规律 语言特点：准确、简明扼要、客观正式,词汇,Unit 1-Grammer(2),大量使用专业词汇和半专业词汇；例c
10、alculus,bandwidth,flip-flop，series,work,大量使用词缀和词根；例tele-,较多使用缩略词;例 PCM，CDMA,DSP,词性变换多。例sound,词法,常用一般现在时态，表示真理或客观规律的陈述。,矢量和矩阵方法为现代工程学的发展提供了框架。,例1 Vector and matrix techniques provide the framework for much of the developments in modern engineering.,广泛使用被动语态，强调所论述的客观事物。,第7章和第8章讨论单变量函数的微积分，考虑到学生数学基础参差不
11、齐，第7章复习微分与积分的基本概念与方法。,例2 Chapters 7and 8 are devoted to the calculus of functions of one variable and,recognizing again the mixed background knowledge in mathematics of the students,the basicideas and techniques of differentiation and integration are reviewed in Chapter 7.,Unit 1-Grammer(3),词法,普遍使用名
12、词词组及名词化结构，强调客观存在的事实而非某一行为，故常使用表示动作或状态的抽象名词。,电视通过无线电波发射和接收移动物体的图像。,例3 Television is the transmission and reception of images of moving objects by radio waves.,使用非限定动词，使句子简明。,微积分辅以解析几何是一个非常强大的工具，能够解决许多困扰已久甚至以前认为无法解决的问题。,例4 The calculus,aided by analytic geometry,proved to be astonishingly powerful and
13、 capable of attacking hosts of problems that had been baffling and quite unassailable in earlier days.,Unit 1-Grammer(4),句法,Unit 1-Grammer(5),较常使用“无生命主语+及物动词+宾语（+宾语补足语）”句型。,第6章介绍序列、级数及极限等基本概念。,例5 Chapter 6 provides a basic introduction to the ideas of sequences,series andlimits.,常用it做形式主语或形式宾语。,已经证明
14、，感应电压使电流的方向与产生电流的磁场力方向相反。,例6 It has been proved that induced voltage causes a current to flow in opposition to the force producing it.,例7 The invention of radio has made it possible for mankind to communicate with each other over a long distance.,无线电的发明使人类有可能进行远距离通信。,Unit 1-Grammer(6),尽量用紧缩型状语从句而不用完
15、整句。,尽管本书主要为工科学生所用，我们相信，它也非常适合于修读物理与应用数学的学生。,例8 While designed primarily for use by engineering students,it is believed that the book is also highly suitable for students of the physical sciences and applied mathematics.,割裂修饰比较普遍（包括短语或从句被分隔）。,希望这些练习，以及书中提供的大量实例及本书的写作风格也使本书适于自学和课堂教学。,例9 It is hoped th
16、at this provision,together with thelarge number of worked examples and style of presentation,also makes the booksuitable for private or directed study.,句法,Unit 1-Grammer(7),句法,较多使用祈使语气。,设前向传递函数由线性差分方程给出。,例10 Let the forward-pass transfer function be given by the linear difference equation.,句中并列成分（各种
17、并列短语、单词或从句）较多。,与光波检测系统相比，雷达具有如下优点：（1）检测范围广；（2）可全天候使用；（3）拥有先进的电子元器件与电子线路，可用于信号的发射、接收、放大、检测和测量。,例11 Radar has certain inherent advantages over detection systems employing light waves:(1)it has greater range,(2)it is usable in any weather and in day or night,and(3)the electronic circuitry and component
18、s for transmitting,receiving,amplifying,detecting and measuring are highly developed.,Unit 1-Grammer(8),句法,复杂长句多。科学技术要阐明事物之间错综复杂的关系，因而需要用复杂的语法关系来表达严密复杂的思维。长句所表达的科技内容严密性、准确性和逻辑性较强。,分析与设计过程中常用数值计算方法来弥补解析法的不足，因此在求解复杂的工程问题 时数值方法往往是最为恰当的。由于认识到数值方法在工程实践中的应用日趋增长，人们普遍认为它应该被整合到数学课程中来。,例12 Recognizing the inc
19、reasing use of numerical methods in engineering practice,which often complement the use of analytical methods in analysis and design and are ofultimate relevance when solving complex engineering problems,there is wideagreement that they should be integrated within the mathematics curriculum.,The End
20、 of Unit 1,Unit 2-Text(1),Words&Expressionsadvocate 5AdvEkit n.主张者，赞成者alternative C:l5tE:nEtiv adj.另一个可选择的argument 5B:jumEnt n.自变量concentration 7kCnsen5treiFEn n.集中，集合，浓缩converge kEn5vE:dVv.收敛（n.convergence）deficiency di5fiFEnsi n.缺乏，不足derivative di5rivEtiv n.导数die dai n.骰子differentiable 7difE5renFi
21、Ebl adj.可微分的disperse dis5pE:s v.（使）分散，（使）散开，疏散facility fE5siliti n.设备，工具histogram 5histEurAm n.直方图,inference 5infErEns n.推论interpretation in5tE:prEteiFEn n.说明，解释profile 5prEufail n.剖面，侧面，外形，轮廓proportion prE5pC:FEn n.比例pseudo-random 5psju:dEu 5rAndEm adj.伪随机的refraction ri5frAkFEn n.折射stabilize 5steIb
22、IlaIz v.稳定（n.stabilization）statistical stE5tistikEl adj.统计的，统计学的stochastic stEu5kAstik adj.随机的successive sEk5sesiv adj.连续的toss tCs v.;n.投，掷underlie 7QndE5lai v.位于之下，成为的基础,Unit 2-Text(2),by means of 依靠consist of 由组成give rise to 引起，使发生in contrast with 和形成对比对照in terms of根据，按照，用的话，在方面Bernoulli distribut
23、ion 伯努利分布Binomial distribution 二项式分布Normal distribution 正态分布Poisson distribution 泊松分布probability density function 概率密度函数（abbr.pdf）Uniform distribution 均匀分布,Unit 2-Text(3),Notes1 This concept of probability is of an objective quantitythat applies to each observation and measures(in a relative way)how
24、 likely it isto fall into the corresponding class.,Unit 2-Text(4),“be of”这种结构用来表示人或物的特征，通常译为“具有”。,概率的这种定义是客观的，它应用于每次观测，并以一种相对的方式度量其结果归入相应类别的可能性。,Notes2 It seems that one is forced into a subjective view of the un-certainties,but theprobability figures that emerge must obey certain rules in order to
25、be consistent.,Unit 2-Text(5),“that emerge”是定语从句，修饰先行词figures（数字）。,看来，人们对这种不确定性陷入了自己的主观判断中，但是由此产生的概率必须遵循某些准则以保持一致性。,Notes3 Forengineering students it is most appropriate to keep the first interpretationthatof probability as an idealized proportionin mind when studying the theory.,Unit 2-Text(6),“tha
26、t of”补充说明interpretation,that即指interpretation,它们将 keep in mind分隔。,对于工科学生，学习概率论时应谨记，概率就是理想的比例。,Notes4 This may seem a hopeless requirement,consideringthat computer programs are sequences of deterministic instructions running ondeterministic hardware.,Unit 2-Text(7),“considering that”引导原因状语从句。,由于计算机程序是
27、在确定的硬件上运行的确定的指令，这似乎是个奢求。,Notes5 The successive variables appear to be uncorrelated,and,al-thoughthere is some structure in the sequence(and indeed the sequence will eventuallyrepeat itself),it is rare for these deficiencies to cause problems in practice.,Unit 2-Text(8),“the successive variables”是指序列
28、中的变量，强调个体，而“the sequence”则是指 这个序列，强调整体。,序列 中的元素看似互不相关，尽管在序列中存在某些结构（该序列最终的确会重复），但这并不影响实际应用。,Unit 2-Grammer(1),专业英语词汇,专业词汇（technical words）指在某一学科、某一专业所独有的专用术语，只有一种专业含义，非常单纯，如histogram，probability，oscillator等。,半专业词汇（semi-technical words）指跨学科出现的频率很高的词，在不同的专业领域具有不同的精确含义，如carrier 等。,非专业词汇（non-technical wo
29、rds）指在非专业英语中很少使用，却严格属于非专业英语性质的词汇，如application,implementation,to yield等。,构词法,主要包括：派生、复合、转化、拼缀和缩略等。,1.派生法（Derivation）,派生法通过在原有词或词根的基础上加前缀或（和）后缀而构成新词，前缀通常用以修饰或改变词意，后缀显示词性。表2.1表2.4分别列出电子与通信专业常用的前后缀及词根。,表2.1 常用前缀,Unit 2-Grammer(2),1.派生法（Derivation）,续表2.1,Unit 2-Grammer(3),1.派生法（Derivation）,表2.2 表示数量关系的常用
30、前缀,Unit 2-Grammer(4),1.派生法（Derivation）,表2.3 常用后缀,Unit 2-Grammer(5),1.派生法（Derivation）,续表2.3,Unit 2-Grammer(6),1.派生法（Derivation）,表2.4 常用词根,Unit 2-Grammer(7),2.复合法（Composition）,Unit 2-Grammer(8),复合法是由两个或两个以上的词按照一定的次序排列，以构成新词。多数复合词可通过其组成部分猜测词意。例如，trial and error（反复试验），Q-factor（品质因子），allowable error（允许误差
31、）等。此外，常采用以下两种形式构成复合词：,直接结合，如breakthrough（突破）,overestimate（高估）,bandwidth（带宽）等；,用连字符结合，如general-purpose（多种用途的）,state-of-the-art（达到最新技术发展水平的）等。,Unit 2-Grammer(9),转换法即单词词性转换，词性转换后其意义与原意有着密切联系，如function,sound，ground等词。有些词还会发生音变，如use,record等；或音移，如increase,research,subject等。,3.转化法(Conversion),4.拼缀法(Blendin
32、g),拼缀法以原有的两个或两个以上的词为基础，经过首尾剪裁（或保留其中一个原词），重新组合而成，是复合词的缩略形式，如transistor（晶体管）=transfer+resistor,modem（调制解调器）由modulator和demodulator拼缀而成。,Unit 2-Grammer(10),5.缩略法（Shorting）,缩略法是将几个单词的首字母以大写形式缩合到一起成为一个新词。该法多用于专有名词，利于记忆。如radar(RAdio Detection And Ranging，雷达)，GPS(Global Positioning System，全球定位系统)等。,随着电子信息及通
33、信类专业技术日新月异的发展，不断有新的专业词汇出现。大多数新词都是用以上五种传统的构词法构成，掌握了基本词汇，运用构词知识，一方面可提高记忆效率，扩大词汇量，另一方面还可以逆向利用构词知识分解单词，了解单词的来历及新添含义，消除阅读障碍。,The End of Unit 2,Unit 3-Text(1),Words&Expressionsbuffer 5bQfEn.缓冲器by-product 5baIprRdQkt n.副产品，出乎意料的结果circuitry 5sE:kitri n.电路，线路formula 5fC:mjulE n.公式，规则fulcrum 5fQlkrEm n.杠杆的支点g
34、round raund v.使接地 n.接地，地线impedance im5pi:dEns n.阻抗infinitesimal in7finE5tesimEl adv.无穷小，极小，无限小inherent in5hiErEnt adj.固有的，内在的，与生俱来的intuitive in5tju(:)itiv adj.直觉的investigate in5vestieit v.调查，研究latch lAtF v.闭锁（n.锁存器）lever 5li:vE,5levE n.杆，杠杆mythical 5miWikEl adj.神话的，虚构的offset 5C:fset n.偏移量，抵消polarity
35、 pEu5lAriti n.极性,potential pE5tenFEln.电势，电位restraint ris5treintn.约束（条件）rote rEut n.死记硬背，机械的做法，生搬硬套saturation 7sAtFE5reiFEn n.饱和（状态），饱和度stability stE5bilitin.稳定性unity 5ju:niti n.统一，一致variation 7vZEri5eiFEn n.变更，变化，变异，变种closed loop gain闭环增益differential input amplifier差分放大器inverting input反相输入端ideal ope
36、ration amplifier 理想运放（abbr.ideal op amp）phase shift相移voltage follower射极跟随器,Unit 3-Text(2),Notes1 Frequency response will beflat and bandwidth infinite because AC will be simply a rapidly varying DC level to the idealamplifier.,Unit 3-Text(3),bandwidth 后省略 will be。,对于理想放大器而言，交流只不过是快速变化的直流，所以其频率响应是一条水
37、平直线，带宽无限。,Notes2 An important by-product of these properties of the ideal operational amplifier is that the summingpoint,the inverting input,will conduct no current to the amplifier.,Unit 3-Text(4),the inverting input 是 the summing point 的同位语，表示相同的意思，翻译时可以省略。,由理想运放的特性可以得出一个很重要的结论，即放大器的反相输入端无电流流过。,No
38、tes3 Though the ideal model may seem a bit remotefrom realitywith infinite gain,bandwidth,etc.,it should be realized that the closed loop gainrela-tions which will be derived in this section are directly applicable to real circuitsto within afew tenths of a percent in most cases.,Unit 3-Text(5),with
39、结构对从句中的主语the ideal model予以补充说明，a few tenth of 表示“十分之几”的意思。,尽管理想模型与实际电路相差甚远，比如，理想运放具有无限带宽和无穷大的增益，但需要明白的是，本节利用理想运放推导出的闭环增益公式可直接应用于实际电路，多数情况下两者相差仅为千分之几。,Notes4 If a small voltage,measured at theinverting input with respect to the non-inverting input,is assumed to exist,the amplifier outputvoltage will
40、be of opposite polarity and can always increase in value(with infinite outputavailable)until the voltage between the inputs becomes infinitesimally small.,Unit 3-Text(6),句中的opposite是相对于从句中的主语a small voltage而言。,假如在反相输入端测得与同相输入端之间存在一小电压，则放大器的输出电压与该输入电压极性相反且其数值会一直增加（可以是无穷大），直至输入电压变为无穷小为止。,Notes5 In con
41、trol andinstrumentation applications,its practical value lies in the ease with which desired inputimpedance and gain values can be tailored to fit the requirements of the associated circuitry.,Unit 3-Text(7),lie in表示原因，the ease with which 中的 which 指代 ease,with ease 等效于 easily。,在控制与仪器仪表应用中，反相放大器的实用价值
42、在于，利用它可以很容易地调整所需的输入阻抗和增益值以适应相关电路的要求。,科技文章中，数字频繁出现，用阿拉伯数字比用单词陈述更有利。但出现下述情形时须遵循约定俗成的规则：用单词表示不定数量或近似值；句首不用阿拉伯数字，一般用英语的单词，句末要尽量避免用阿拉伯数字；两数连用时，分别用单词和阿拉伯数字表示，习惯上将短的用单词写出；遇到分数，可用带连字符号的单词表示，等等。如：,Unit 3-Grammer(1),数量的表示,1.数字的表示,例1 Phase shift is 180.,（输出电压与输入电压的）相移为180。,例2 The gain of the voltage follower w
43、ith the feedback loop closed(closed loop gain)is unity.,电压跟随器的闭环增益为1。,2.不确定数字的表示,Unit 3-Grammer(2),大约、左右，常用about/some/approximately/of the order of/more or less/or so等词；,多于，常用over,above,more than,in excess of 等词；,少于，常用less than,under,below,close to等词；,以复数形式表示，如tens/dozens/scores/hundreds/thousands o
44、f,thousands upon thousands of等。,2.不确定数字的表示,表3.1 某些表示数量的词和词组,Unit 3-Grammer(3),of,2.不确定数字的表示,例3 The result indicated that actual error probabilities were of the order of 1 percent.,例4 The microwave communication channel has a very large bandwidth and will accommodate thousands of telephone conversati
45、ons or dozens of television channels at once.,结果表明实际误差概率约为1%。,微波通信信道带宽很宽，可同时容纳几千个电话通话或几十个电视信道。,Unit 3-Grammer(4),3.习惯短语,Unit 3-Grammer(5),例5 Economies associated with computer-on-a-chip have resulted in the avail-ability of micro-computer systems with the functionality and performance of minicompute
46、r systems costing two orders of magnitude more only a decade ago.,随着单片机的发展，目前微机系统所拥有的功能及性能可以媲美十年前的小型机，而价格却下降了两个数量级以上。,电路中某部分的电阻等于它两端的电压与流过该部分电路的电流的比值。,例6 The resistance of a given section of an electric circuit is equal to the ratio of its voltage to the current through this section of the circuit.,
47、例7 It is found that the heat energy developed in any conductor is proportional to(is in proportion to)the square of the current,the resistance of the conductor and the time.,人们发现，导体中所产生的热能与电流的平方、导体的电阻值和时间成正比。,Unit 3-Grammer(6),倍数的增减在汉语与英语中的表述有较大的差异，在汉语中增加可以是倍数分数，而减少则只能是分数，而倍数的增减又常常涉及到是否将基数计入其中，所以需要仔
48、细领会。,例8 The power density from a transmitter measured 1m from an isotropic antenna is four times as large as the power density measured 2m from the same antenna.,在离各向同性天线1米远测量的功率密度是离其2米测量的功率密度的4倍。,4.倍数增减,Unit 3-Grammer(7),4.倍数增减,倍数增减的词+ntimes/to ntimes/n-fold/byafactorofn，译为“增加到n倍，或增加了n1倍，减少到1/n，或减少
49、(n1)/n”,集成电路的产量比去年增加了两倍。,例9 The production of ICs has been increased to three times as compared with last year.,例10 The switchingtimeofthenew-typetransistorisshortened3times.,例11 An algorithm is given that reduces the number of multiplications by almost a factor of two but increases the number of ad
50、ditions.,新型晶体管的开关时间缩短了2/3（即缩短到原来的1/3）。,给出的新算法中，乘法数减少了一半而加法数却有所增加。,Unit 3-Grammer(8),4.倍数增减,ann timesn-fold+表示增减的名词，应译为：增加n倍（或增至n倍），或减少到1/n，减少(n1)/n,新手机的主要优点是功耗降低了3/4。,例12 Theprincipaladvantageofthenew type mobileisafour-foldreductioninpower dissipation.,增加一倍、两倍、三倍分别用double（是的两倍），treble（是的三倍），quadrup
