1－A What is mathematics
Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。反过来，数学服务于实践，并在各个领域中起着非常重要的作用。没有应用数学，任何一个现在的科技的分支都不能正常发展。From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry, trigonometry and algebra, in which only the constants are considered.很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on.17世纪工业的快速发展推动了经济技术的进步，从而遇到需要处理变量的问题，从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分，他们都属于高等数学，现在高等数学里面有很多分支，其中有数学分析，高等代数，微分方程，函数论等。Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas ,figures and charts are full of different symbols. Some of the best known symbols of mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition, subtraction , multiplication, division and equality.数学家研究的是概念和命题，公理，公设，定义和定理都是命题。符号是数学中一个特殊而有用的工具，常用于表达概念和命题。公式，图表都是不同的符号……..The conclusions in mathematics are obtained mainly by logical deductions and computation. For a long period of the history of mathematics, the centric place of mathematics methods was occupied by the logical deductions. Now , since electronic computers are developed promptly and used widely, the role of computation becomes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work that merely could be done earlier by logical deductions, for example, the proof of most of geometrical
theorems.数学结论主要由逻辑推理和计算得到，在数学发展历史的很长时间内，逻辑推理一直占据着数学方法的中心地位，现在，由于电子计算机的迅速发展和广泛使用，计算机的地位越来越重要，现在计算机不仅用于处理大量的信息和数据，还可以完成一些之前只能由逻辑推理来做的工作，例如，大多数几何定理的证明。
1－B Equation1
An equation is a statement of the equality between two equal numbers or number symbols. Equation are of two kinds---- identities and equations of condition.An arithmetic or an algebraic identity is an equation. In such an equation either the two members are alike. Or become alike on the performance of the indicated operation.等式是关于两个数或者数的符号相等的一种描述。等式有两种－恒等式和条件等式。算术或者代数恒等式是等式。这种等式的两端要么一样，要么经过执行指定的运算后变成一样。An identity involving letters is true for any set of numerical values of the letters in it.An equation which is true only for certain values of a letter in it, or for certain sets of related values of two or more of its letters, is an equation of condition, or simply an equation. Thus 3x-5=7 is true for x=4 only; and 2x-y=0 is true for x=6 and y=2 and for many other pairs of values for x and y.含有字母的恒等式对其中字母的任一组数值都成立。一个等式若仅仅对其中一个字母的某些值成立，或对其中两个或着多个字母的若干组相关的值成立，则它是一个条件等式，简称方程。因此3x-5=7仅当x=4 时成立，而2x-y=0，当x=6,y=2时成立，且对x, y的其他许多对值也成立。A root of an equation is any number or number symbol which satisfies the equation.There are various kinds of equation. They are linear equation, quadratic equation, etc.方程的根是满足方程的任意数或者数的符号。方程有很多种，例如：线性方程，二次方程等。To solve an equation means to find the value of the unknown term. To do this , we must, of course, change the terms about until the unknown term stands alone on one side of the equation, thus making it equal to something on the other side. W e then obtain the value of the unknown and the answer to the question. To solve the equation, therefore, means to move and change the terms about without making the equation untrue, until only the unknown quantity is left on one side ,no matter which side.解方程意味着求未知项的值，为了求未知项的值，当然必须移项，直到未知项单独在方程的一边，令其等于方程的另一边，从而求得未知项的值，解决了问题。因此解方程意味着进行一系列的移项和同解变形，直到未知量被单独留在方程的一边，无论那一边。Equation are of very great use. W e can use equation in many mathematical problems. W e may notice that almost every problem gives us one or more statements that something is equal to something, this gives us equations, with which we may work if we need it.方程作用很大，可以用方程解决很多数学问题。注意到几乎每一个问题都给出一个或多个关于一个事情与另一个事情相等的陈述，这就给出了方程，利用该方程，如果我们需要的话，可以解方程。
2－A Why study geometry?
Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is
evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools.许多居于领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的受益，许多学校把几何的学习作为入学考试的先决条件，从这一点上可以证明。Geometry had its origin long ago in the measurement by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning “earth” and metron, meaning “measure” . As early as 2000 B.C. we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry .几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地，希腊语几何来源于geo ，意思是”土地“，和metron 意思是”测量“。公元前2000年之前，我们发现这些民族的土地测量者利用几何知识重新确定消失了的土地标志和边界。
2－B Some geometrical terms
A solid is a three-dimensional figure. Common examples of solids are cube, sphere, cylinder, cone and pyramid.A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. A plane surface has two dimensions, length and width. The surface of a blackboard or of a tabletop is an example of a plane surface.立体是一个三维图形，立体常见的例子是立方体，球体，柱体，圆锥和棱锥。立方体有6个面，都是光滑的和平的，这些面被称为平面曲面或者简称为平面。平面曲面是二维的，有长度和宽度，黑板和桌子上面的面都是平面曲面的例子。
3－A Notations for denoting sets
The concept of a set has been utilized so extensively throughout modern mathematics that an understanding of it is necessary for all college students. Sets are a means by which mathematicians talk of collections of things in an abstract way.
Sets usually are denoted by capital letters; elements are designated by lower-case letters.
集合论的概念已经被广泛使用，遍及现代数学，因此对大学生来说，理解它的概念是必要的。集合是数学家们用抽象的方式来表述一些事物的集体的工具。集合通常用大写字母表示，元素用小写字母表示。W e use the special notation to mean that “x is an element of S” or “x belongs to S”. If x does not belong to S, we write .
When convenient, we shall designate sets by displaying the elements in braces; for example, the set of positive even integers less than 10 is displayed as {2,4,6,8} whereas the set of all positive even integers is displayed as {2,4,6,…}, the three dots taking the place of “and so on.”
我们用专用记号来表示x是S的元素或者x属于S。如果x不属于S，我们记为。如果方便，我们可以用在大括号中列出元素的方式来表示集合。例如，小于10的正偶数的集合表示为{2,4,6,8}，而所有正偶数的集合表示为{2,4,6,…}, 三个圆点表示“等等”。
The dots are used only when the meaning of “and so on” is clear. The method of listing the members of a set within braces is sometimes referred to as the roster notation.
The first basic concept that relates one set to another is equality of sets:
只有当省略的内容清楚时才能使用圆点。在大括号中列出集合元素的方法有时被归结为枚举法。
联系一个集合与另一个集合的第一个基本概念是集合相等
DEFINITION OF SET EQUALITY Two sets A and B are said to be equal (or identical) if they consist of exactly the same elements, in which case we write A=B. If one of the sets contains an element not in the other, we say the sets unequal and we write A≠B.
集合相等的定义如果两个集合A和B确切包含同样的元素,则称二者相等，此时记为A=B。如果一个集合包含了另一个集合以外的元素，则称二者不等，记为A≠B。
EXAMPLE 1. According to this definition, the two sets {2,4,6,8} and {2,8,6,4} are equal since they both consist of the four integers 2,4,6 and 8. Thus, when we use the roster notation to describe a set, the order in which the elements appear is irrelevant.
根据这个定义，两个集合{2,4,6,8}和{2,8,6,4}是相等的，因为他们都包含了四个整数2,4,6,8。因此，当我们用枚举法来描述集合的时候，元素出现的次序是无关紧要的
EXAMPLE 2. The sets {2,4,6,8} and {2,2,4,4,6,8} are equal even though, in the second set, each of the elements 2 and 4 is listed twice. Both sets contain the four elements 2,4,6,8 and no others; therefore, the definition requires that we call these sets equal.
This example shows that we do not insist that the objects listed in the roster notation be distinct. A similar example is the set of letters in the word Mississippi, which is equal to the set {M,i,s,p}, consisting of the four distinct letters M,i,s, and p
例2. 集合{2,4,6,8} 和{2,2,4,4,6,8}也是相等的，虽然在第二个集合中，2和4都出现两次。两个集合都包含了四个元素2,4,6,8，没有其他元素，因此，依据定义这两个集合相等.
这个例子表明我们没有强调在枚举法中所列出的元素要互不相同。一个相似的例子是，在单词Mississippi中字母的集合等价于集合{M,i,s,p}, 其中包含了四个互不相同的字母M,i,s,和p.
3－B Subsets
From a given set S we may form new sets, called subsets of S. For example, the set consisting of those positive integers less than 10 which are divisible by 4 (the set {4,8}) is a subset of the set of all even integers less than 10. In general, we have the following definition.
一个给定的集合S可以产生新的集合，这些集合叫做S的子集。例如，由可被4除尽的并且小于10的正整数所组成的集合是小于10的所有偶数所组成集合的子集。一般来说，我们有如下定义。
In all our applications of set theory, we have a fixed set S given in advance, and we are concerned only with subsets of this given set. The underlying set S may vary from one application to another; it will be referred to as the universal set of each particular discourse. （35页第二段）
当我们应用集合论时，总是事先给定一个固定的集合S，而我们只关心这个给定集合的子集。基础集可以随意改变，可以在每一段特定的论述中表示全集。
To avoid logical difficulties, we must distinguish between the elements x and the set {x} whose only element is x. In particular, the empty set is not the same as the set .
In fact, the empty set contains no elements, whereas the set has one element. Sets consisting of exactly one element are sometimes called one-element sets.
为了避免遇到逻辑困难，我们必须区分元素x和集合{x}，集合{x}中的元素是x。特别要注意的是空集和集合是不同的。
事实上，空集不含有任何元素，而有一个元素。由一个元素构成的集合有时被称为单元素集。
Diagrams often help us visualize relations between sets. For example, we may think of a set S as a region in the plane and each of its elements as a point. Subsets of S may then be thought of the collections of points within S. For example, in Figure 2-3-1 the shaded portion is a subset of A and also a subset of B. （35页第五段）
图解有助于我们将集合之间的关系形象化。例如，可以把集合S看作平面内的一个区域，其中的每一个元素即是一个点。那么S的子集就是S内某些点的全体。例如，在图2-3-1中阴影部分是A的子集，同时也是B的子集。
Visual aids of this type, called Venn diagrams, are useful for testing the validity of theorems in set theory or for suggesting methods to prove them. Of course, the proofs themselves must rely only on the definitions of the concepts and not on the diagrams.
这种图解方法，叫做文氏图，在集合论中常用于检验定理的有效性或者为证明定理提供一些潜在的方法。当然证明本身必须依赖于概念的定义而不是图解。
4－A Integers and rational numbers
There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers.
有一些R的子集很著名，因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集，整数集和有理数集。
To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers.
我们从数字1开始介绍正整数，公理4保证了1的存在性。1+1用2表示，2+1用3表示，以此类推，由1重复累加的方式得到的数字1,2,3，…都是正的，它们被叫做正整数。
Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.
严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。
Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set.
虽然这些说法的直观意思似乎是清楚的，但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义，一个简便的方法是先引进归纳集的概念。
DEFINITION OF AN INDUCTIVE SET. A set of real numbers is called an inductive set if it has the following two properties:
The number 1 is in the set.
For every x in the set, the number x+1 is also in the set.
For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set.
现在我们来定义正整数，就是属于每一个归纳集的实数。
Let P denote the set of all positive integers. Then P is itself an inductive set because (a) it contains 1, and (b) it contains x+1 whenever it contains x. Since the members of P belong to every inductive set, we refer to P as the smallest inductive set.
用P表示所有正整数的集合。那么P本身是一个归纳集，因为其中含1，满足(a)；只要包含x就包含x+1, 满足(b)。由于P中的元素属于每一个归纳集，因此P 是最小的归纳集。
This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.
P的这种性质形成了一种推理的逻辑基础，数学家称之为归纳证明，在介绍的第四部分将给出这种方法的详细论述。
The negatives of the positive integers are called the negative integers. The positive integers, together with the negative integers and 0 (zero), form a set Z which we call simply the set of integers.
正整数的相反数被叫做负整数。正整数，负整数和零构成了一个集合Z，简称为整数集。
n a thorough treatment of the real-number system, it would be necessary at this stage to prove certain theorems about integers. For example, the sum, difference, or product of two integers is an integer, but the quotient of two integers need not to ne an integer. However, we shall not enter into the details of such proofs.
在实数系统中，为了周密性，此时有必要证明一些整数的定理。例如，两个整数的和、差和积仍是整数，但是商不一定是整数。然而还不能给出证明的细节。Quotients of integers a/b (where b≠0) are called rational numbers. The set of rational numbers, denoted by Q, contains Z as a subset. The reader should realize that all the field axioms and the order axioms are satisfied by Q. For this reason, we say that the set of rational numbers is an ordered field. Real numbers that are not in Q are called irrational
整数a与b的商被叫做有理数，有理数集用Q表示，Z是Q的子集。读者应该认识到Q满足所有的域公理和序公理。因此说有理数集是一个有序的域。不是
有理数的实数被称为无理数。
4－B Geometric interpretation of real numbers as points on a line
The reader is undoubtedly familiar with the geometric interpretation of real numbers by means of points on a straight line. A point is selected to represent 0 and another, to the right of 0, to represent 1, as illustrated in Figure 2-4-1. This choice determines the scale.
毫无疑问，读者都熟悉通过在直线上描点的方式表示实数的几何意义。如图2-4-1所示，选择一个点表示0，在0右边的另一个点表示1。这种做法决定了刻度。If one adopts an appropriate set of axioms for Euclidean geometry, then each real number corresponds to exactly one point on this line and, conversely, each point on the line corresponds to one and only one real number.
如果采用欧式几何公理中一个恰当的集合，那么每一个实数刚好对应直线上的一个点，反之，直线上的每一个点也对应且只对应一个实数。
For this reason the line is often called the real line or the real axis, and it is customary to use the words real number and point interchangeably. Thus we often speak of the point x rather than the point corresponding to the real number.
为此直线通常被叫做实直线或者实轴，习惯上使用“实数”这个单词，而不是“点”。因此我们经常说点x不是指与实数对应的那个点。
This does not mean that one should not make use of geometry in studying properties of real numbers. On the contrary, the geometry often suggests the method of proof of a particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof (one depending entirely on the axioms for the real numbers).
这并不意味着研究实数的性质时不会应用到几何。相反，几何经常会为证明一些定理提供思路，有时几何讨论比纯分析式的证明更清楚。
In this book, geometric arguments are used to a large extent to help motivate or clarity a particular discuss. Nevertheless, the proofs of all the important theorems are presented in analytic form.
在本书中，几何在很大程度上被用于激发或者阐明一些特殊的讨论。不过，所有重要定理的证明必须以分析的形式给出。
5-A The coordinate system of Cartesian geometry As mentioned earlier, one of the applications of the integral is the calculation of area. Ordinarily we do not talk about area by itself, instead, we talk about the area of something. 就像前面提到的 积分的一个应用就是计算面积. 通常我们不讨论面积本身, 相反, 是讨论某物的面积. This means that we have certain objects (polygonal regions, circular regions, parabolic segments etc.) whose areas we wish to measure. 这意味着我们想测量一些物体的面积 多边形区域 圆域 抛物弓形等。If we hope to arrive at a treatment of area that will enable us to deal with many different kinds of objects, we must first find an effective way to describe these objects. 如果我们希望获得面积的计算方法以便能够用它来处理各种不同类型的图形 我们就必须首先找出表述这些图形的有效方法。The most primitive way of doing this is by drawing figures, as was done by the ancient Greeks. 描述图形最原始的方法是画图, 就像古希腊人做的那样 A much better way was
suggested by Rene Descartes, who introduced the subject of analytic geometry (also known as Cartesian geometry). R.笛卡儿提出了一种好得多的办法 并建立了解析几何 也称为笛卡儿几何 这个学科。Descartes’idea was to represent geometric points by numbers. The procedure for points in a plane is this : 笛卡儿的思想就是用数来表示几何点 在平面上找点的过程如下 Two perpendicular reference lines (called coordinate axes) are chosen, one horizontal (called the “x-axis ”), the other vertical (the “y-axis ”). Their point of intersection, denoted by O, is called the origin. 选两条互相垂直的参考线(称为坐标轴), 其中一条是水平的(称为x轴), 另一条是竖直的(称为y轴). 它们的交点记为O, 称为原点. On the x-axis a convenient point is chosen to the right of O and its distance from O is called the unit distance. 在x轴上 原点的右侧选择一个合适的点 该点与原点之间的距离称为单位长度。V ertical distances along the y-axis are usually measured with the same unit distance, although sometimes it is convenient to use a different scale on the y-axis. 沿着y轴的竖直距离通常用同样的单位长度来测量 不过有时采用不同的尺度(单位长度)较为方便。Now each point in the plane (sometimes called the xy-plane) is assigned apair of numbers, called its coordinates. These numbers tell us how to locate the points. 现在xy平面上的每一个点都分配了一对数, 称为坐标. 这些数告诉我们如何定义一个点。The x-coordinate of a point is sometimes called its abscissa and the y-coordinate is called its ordinate. (P47第一段最后一句) 有时将一个点的x坐标称为横坐标 y坐标称为纵坐标。When we write a pair of numbers such as (a, b) to represent a point in a plane, we agree that the abscissa or x-coordinate a is written first. (P47第二段第一句) 当用一对数(a, b)来表示平面的点时 商定要把横坐标或者x坐标写在第一个位置上。The procedure for points in space is similar. W e take three mutually perpendicular lines in space intersecting at a point (the origin). 在空间中找点的过程是相似的。在空间中选取相交于一点的三条互相垂直的直线。These lines determine three mutually perpendicular planes, and each point in space can be completely described by specifying, with appropriate regard for signs, its distances from these planes. 这三条线确定了三个互相垂直的平面, 考虑用恰当的符号表示空间中的一个点到这些平面的距离 就可以完整地描述这个点。W e shall discuss three-dimensional Cartesian geometry in more detail later on; for the present we confine our attention to plane analytic geometry. 以后我们将更加详细地讨论三维笛卡儿几何学。目前将注意力集中于平面解析几何。5-B Geometric figures A geometric figure, such as a curve in the plane , is a collection of points satisfying one or more special conditions. 一个几何图形是满足一个或多个特殊条件的点集 比如平面上的曲线。By translating these conditions into expressions, involving the coordinates x and y, we obtain one or more equations which characterize the figure in question. 通过把这些条件转化成含有坐标x和y的表达式 我们就得到了一个或多个能刻画该图形特征的方程Throughout their historical development, calculus and analytic geometry have been intimately intertwined. 微积分与解析几何在它们的发展史上已经紧密地融合在一起了。New discoveries in one subject led to improvements in the other. The development of calculus and analytic geometry in this book is similar to the historical development, in that the
two subjects are treated together. 一门学科的新发现会导致另一门学科的进步。本书中所叙述的微积分和解析几何的发展和历史发展过程是相似的 因为这两门学科是一起研究的。However, our primary purpose is to discuss calculus. Concepts from analytic geometry that are required for this purpose will be discussed as needed. 不过 我们的主要目的是讨论微积分。为此 解析几何中的概念将只是在必要时讨论。Actually, only a few very elementary concepts of plane analytic geometry are required to understand the rudiments of calculus. 实际上 仅仅在微积分入门阶段需要用到平面解析几何的几个基本概念。A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and this study will be carried out using vector method. 如果想拓展微积分的范围与应用 需要进一步研究解析几何 而这种研究需用到向量的方法来实现。Until then, all that is required from analytic geometry is a little familiarity with drawing graph of function. 而这之前 关于解析几何仅仅需要熟悉一点画函数图象的知识。
6-A Informal description of functions
Various fields of human have to do with relationships that exist between one collection of objects and another.
各行各业的人们都必须处理一类事物与另一类事物之间存在的关系。Graphs, charts, curves, tables, formulas, and Gallup polls are familiar to everyone who reads the newspapers.
几乎每个人都熟悉图形，图表，曲线，公式和盖洛普民意测验。
These are merely devices for describing special relations in a quantitative fashion. Mathematicians refer to certain types of these relations as functions. 这些只是以定量的方式描述特定关系的方法。数学家将这些关系中的某些类型视作函数。In this section, we give an informal description of the function concept. A formal definition is given in Section 3.
在本节中，我们给出一个非正式的描述函数的概念。在第3节给出一个正式的定义。
EXAMPLE 1. The force F necessary to stretch a steel spring a distance x beyond its natural length is proportional to x. That is, F=cx, where c is a number independent of x called the spring constant.
把一个钢制的弹簧拉伸到超过其自然长度的距离为x时所需要的力F与x成正比。即，F=cx,这里c是不依赖与x的数，叫做弹性系数。
This formula, discovered by Robert Hooke in the mid-17th century, is called Hooke’s law, and it is said to express the force as a function of the displacement. 这个公式是在17世纪中叶被胡克发现的，叫做胡克定律，它用来表示力关于位移的函数。
EXAMPLE 2. The volume of a cube is a function of its edge-length. If the edges have length x, the volume V is given by the formula V=x3.
立方体的体积是它棱长的函数。如果棱长为x，那么体积的公式为：V=x3。EXAMPLE 3. A prime is any integer n>1 that cannot be expressed in the form n=ab, where a and b are positive integers, both less than n. The first few primes are 2,3,5,7,11,13,17,19.
素数是大于1且不能表示成n=ab形式的整数，这里a和b都是小于n的正整数。
开始的几个素数是2,3,5,7,11,13,17,19.
For a given real number x>0, it is possible to count the number of primes less than or equal to x. This number is said to be a function of x even though no simple algebraic formula is known for computing it (without counting) when x is known.
对于一个给定的实数x>0，数出小于或者等于x的素数的个数是有可能的。这个数称为x的函数，尽管还没有一个简单代数式可以由已知的x计算(不通过计数求)出它的值。
The word “function”was introduced into mathematics by Leibniz, who used the term primarily to refer to certain kinds of mathematical formulas.
“函数”这个词是由莱布尼茨引入到数学中的，他主要使用这个术语来指代某种数学公式。
It was later realized that Leibniz’s idea of function was much too limited in its scope, and the meaning of the word has since undergone many stages of generalization.
后来人们才认识到，莱布尼茨的函数思想适用的范围太过局限了，这个术语的含义从那时起已经过了多次推广。
Today, the meaning of function is essentially this: Given two sets, say X and Y, a function is a correspondence which associates with each element of X one and one only element of Y.
如今，从本质上讲，函数的定义如下：给定两个集合X 和Y，函数是X中元素与Y中元素的一一对应。
The set X is called the domain of the function. Those elements of Y associated with the elements in X form a set called the range of the function. (This may be all of Y, but it need not be)
集合X叫做函数的定义域，与X中的元素相对应的Y中的元素的集合叫做函数的值域。(值域可能是整个集合Y,也可能不是。)
Letters of the English and Greek alphabets are often used to denote functions. The particular letters f,g,h,F,G,H, and are frequently used for this purpose.
英语字母和希腊字母表通常用于表示函数。为此，一些特定的字母如：f,g,h,…频繁使用。
If f is a given function and if x is an object of its domain, the notation f(x) is used to designate that object in the range which is associated to x by the function f; and it is called the value of f at x or the image of x under f. The symbol f(x) is read as “f of x.”如果f是一个给定的函数，x是它定义域中的一个点，符号f(x)表示值域中按照f对应于x的点，它叫做f在x点的值或者x在f下的像。符号f(x)读作“f of x.”
7-A The definition of sequences
n everyday usage of the English language, the words “sequence”and “series”are synonyms, and they are used to suggest a succession of things or events arranged in some order.
在日常英语中，单词“sequence”和“series”是同义词，用以表示按某种次序排列的一串东西或事件。In mathematics these words have special technical meanings.在数学中这些单词有特殊的专业含义。The word “sequence”is
employed as in the common use of the term to convey the idea of a set of things arranged in order, but the word “series”is used in a somewhat different sense.像通常用法一样，术语“sequence”用以表达按次序排列的一串东西的意思，但是“series”一词则用于表示别的意思（级数）。The concept of a sequence will be discussed in this section, and series will be defined in section 11.序列的概念在本节讨论，级数的概念将在第11节定义If for every positive integer n there is associated a real or complex number an, then the ordered set a1 , a2, …, an ,…is said to define an infinite sequence.
如果对每一个正整数n都有一个实数或复数an与之对应, 则有序集a1 , a2, …, an ,…称为一个无穷序列. The important thing here is that each member of the set has been labeled with an integer so that we may speak of the first term a1, the second term a2, and, in general, the nth term an. 这里重要的是集合中的每一个元素都由一个整数标记，因此我们可以说第一项, 第二项, 一般的，第n 项。Each term has a successor and hence there is no “last ”term.
每一项都有下面的一项，因此没有最后一项。The most common examples of sequences can be constructed if we give some rule or formula for describing the nth term. 如果我们给出描述第n项的规则或者公式，就可以构造出序列的常见例子。Another common way to define a sequence is by a set of instructions which explains how to carry on after a given start. Thus we may have a1=a2=1, an+1=an+an-1 for n ≥2 .另一种常用的定义序列的方法是，通过一串指令说明在给定首项后如何给出后面的各项。This particular rule is known as a recursion formula and it defines a famous sequence whose terms are called Fibonacci numbers. The first few terms are 1,1,2,3,5,8,13,21,34.这个特殊的规则就是常见的递推公式，它定义了一个著名的序列，其中的项称为菲波那契数。前几项是…...※In any sequence the essential thing is that there be some function f defined on the positive integers such that f(n) is the nth term of the sequence for each n=1,2,3,…对任意序列，最本质的事就是存在某一个定义在正整数集上的函数，使得对n=1,2,3,…f(n) 为序列的第n项
In fact, this is probably the most convenient way to state a technical definition of sequence. 事实上，这可能是给出序列专业定义的一种最方便的方法。DEFINITION. A function f whose domain is the set of all positive integers 1,2,3,…is called an infinite sequence. The function value f(n) is called the nth term of the sequence.定义域为所有正整数集合的函数f 被称为无穷序列。函数值f(n) 称为序列的第n项。The range of the function (that is, the set of function values) is usually displayed by writing the terms in order. 函数的值域（即是函数值的集合）通常以按顺序书写各项的方式来表示。V ery often the dependence on n is denoted by using subscripts, and we write an, xn…, or something similar instead of f(n). Unless otherwise specified, all sequences in this chapter are assumed to have real or complex terms. 序列各项对n 的依赖性常利用下标来表示，记为an 或者其他类似的记号，而不记作f(n) 。除非另有说明，本章研究的序列都是假定具有实的项或复的项。
7-B The limit of a sequence
The main question we are concerned with here is to decide whether or not the terms f(n) tend to a finite limit as n increases infinitely. 这里我们关心的主要问
题是当n无限增加时，项f(n)是否会趋于一个有限的极限。
To treat this problem, we must extend the limit concept to sequences. This is done as follows为了解决这个问题，必须把极限的概念推广到序列中。做法如下：DIFINITION. A sequence {f(n)} is said to have a limit L if, for every positive number e, there is another positive number N ( which may depend on e ) such that
| an－L | < e for all n ≥N .
In this case, we say the sequence {f(n)} converges to L. A sequence which does not converge is called divergent.……不收敛的序列被称为发散序列。In this definition the function values f(n) and the limit L may be real or complex numbers. If f and L are complex, we may decompose them into their real and imaginary parts, say f=u+iv and L=a+ib.在这个定义中，函数值f(n) 和极限L都可能是实数或者复数。如果f和L是复数, 可以将其分解为实部和虚部。In other words, a complex-valued sequence f converges if and only if both the real part u and the imaginary part v converge separately.换句话说，复值序列f收敛当且仅当实部和虚部(序列)分别收敛。※It is clear that any function defined for all positive real x may be used to construct a sequence by restricting x to take only integer values.
显然, 每一个对所有正实数x 有定义的函数都可以用来构造一个序列，其办法是限制x 只取整数值。The phrase “convergent sequence”is used only for a sequence whose limit is finite. A sequence with an infinite limit is said to diverge. There are, of course, divergent sequences that do not have infinite limits.仅当一个序列的极限有限时，才使用短语“收敛序列”。一个具有无穷极限的序列称为发散序列。当然，一个发散序列未必存在一个无穷极限。
9-A Introduction
A large variety of scientific problems arise in which one tries to determine something from its rate of change. For example , we could try to compute the position of a moving particle from a knowledge of its velocity or acceleration. Or a radioactive substance may be disintegrating at a known rate and we may be required to determine the amount of material present after a given time.大量的科学问题需要人们根据事物的变化率来确定该事物，例如，我们可以由已知速度或者加速度来计算移动粒子的位置. 又如，某种放射性物质可能正在以已知的速度进行衰变，需要我们确定在给定的时间后遗留物质的总量。In examples like these, we are trying to determine an unknown function from prescribed information expressed in the form of an equation involving at least one of the derivatives of the unknown function . These equations are called differential equations, and their study forms one of the most challenging branches of mathematics.在类似的例子中，我们力求由方程的形式表示的信息来确定未知函数，而这种方程至少包含了未知函数的一个导数。这些方程称为微分方程，对其研究形成了数学中最具有挑战性的一门分支。
The study of differential equations is one part of mathematics that, perhaps more than any other, has been directly inspired by mechanics, astronomy, and mathematical physics.微分方程的研究是数学的一部分，也许比其他分支更多的直接受到力学，天文学和数学物理的推动。
Its history began in the 17th century when Newton, Leibniz, and the Bernoullis solved some simple differential equations arising from problems in geometry and mechanics. These early discoveries, beginning about 1690, gradually led to the development of a lot of “special tricks” for solving certain special kinds of differential equation.微分方程起源于17世纪，当时牛顿，莱布尼茨，波努力家族解决了一些来自几何和力学的简单的微分方程。开始于1690年的早期发现，逐渐引起了解某些特殊类型的微分方程的大量特殊技巧的发展。Although these special tricks are applicable in relatively few cases, they do enable us to solve many differential equations that arise in mechanics and geometry, so their study is of practical importance. Some of these special methods and some of the problems which they help us solve are discussed near the end of this chapter.尽管这些特殊的技巧只是用于相对较少的几种情况，但他们能够解决力学和几何中出现的许多微分方程，因此，他们的研究具有重要的实际应用。这些特殊的技巧和有助于我们解决的一些问题将在本章最后讨论。Experience has shown that it is difficult to obtain mathematical theories of much generality about solution of differential equations, except for a few types.经验表明除了几个典型方程外，很难得到微分方程解的一般性数学理论。
Among these are the so-called linear differential equations which occur in a great variety of scientific problems.在这些典型方程中，有一个称为线性微分方程，出现在大量的科学问题中。
11-A predicatesStatements involving variables, such as “x>3”, ”x+y=3”, ”x+y=z” are often found in mathematical assertion and in computer programs. These statements are neither true nor false when the values of the variables are not specified. In this section we will discuss the ways that propositions can be produced from such statements.包含变量的语句，比如“x>3”, ”x+y=3”, ”x+y=z” 常出现在数学论断中和计算机程序中，若未给语句中的所有变量赋值，则不能判定该语句是真是假，本节要讨论由这种语句生成命题的方法。The statement “x is greater than 3” has two parts. The first part, the variables, is the subject of the statement. The second part-the predicate, “is greater than 3”-refers to a property that the subject of the statement can have.语句“x大于3”分成两部分，第一部分，变量，是语句的主语。第二部分，谓语，“大于3”，指的是语句主语具有的性质。W e can denote the statement “x is greater than 3” by P(x), where P denote the predicate “is greater than 3” and x is the variable. The statement P(x) is also said to be the value of the propositional function P at x. once a value has been assigned to the variable x, the statements P(x) becomes a proposition and has a truth value.把语句“x大于3”记为P(x), 其中P表示谓词“大于3”，而x是变量。语句P(x)也称为命题函数P在x点处的值。一旦赋予x一个值，语句P(x)就成为一个命题,有了真值。
11-B QuantifiersWhen all the variables in a propositional function are assigned values, the resulting statement has a truth value. However, there is another important way, called quantification, to create a proposition from a propositional function. two types of quantification will be discussed here, namely, universal quantification and existential quantification .当命题函数所有变量都赋值时，结果语句有真值，但是还有另外一种方式，称为量词化，可从命题函数中得到命
题。这里讨论两种量词化方法，也就是全称量词化和存在量词化。Many mathematical statements assert that a property is true for all values of a variable in a particular domain, called the universe of discourse. Such a statement is expressed using a universal quantification. The universal quantification of a propositional function is the proposition that assert that P(x) is true for all values of x in the universe of discourse. The universe of discourse specifies the possible values of the variable x.许多数学语句认为，在特殊领域内对变量所有值都成立的性质称为论域。这样的语句可用全称量词化表示。命题函数的全称量词化是一个命题，认为P(x)对论域中x的所有值P(x)都是真的。论域指定变量x的可能取值.
12-A Special terminology peculiar to probability theory
In discussions involving probability, one often sees phrases from everyday language such as “two events are equally likely,” “an event is impossible,” or “an event is certain to occur.” expressions of this sort have intuitive appeal and it is both pleasant and helpful to be able to employ such colorful language in mathematical discussions.在讨论概率论时，会常常从日常用语中看到这样的语句：两个事件是同等可能的，一个事件是不可能的，一个事件肯定发生，这种表达方式非常直观，在数学讨论中，乐于使用这样有色彩的语言，而且使用起来很有帮助。Before we can do so, however, it is necessary to explain the meaning of this language in terms of the fundamental concepts of our theory.但是，在我们这么做之前，有必要根据我们理论的基本概念来解释这种语句的含义。Because of the way probability is used in practice, it is convenient to imagine that each probability space (S,B,P) is associated with a real or conceptual experiment. The universal set S can then be thought of as the collection of all conceivable outcomes of the experiment, as in the example of coin tossing discussed in the foregoing section. 根据概率论实际应用的方式，很方便的把每一个概率空间（S,B,P）对应于一个实际的或者概念上的试验。全集S是试验中所有可信结果的集体，就像前面章节讨论的掷硬币的例子。Each element of S is called an outcome or a sample and the subsets of S that occur in the Boolean algebra B are called events. The reasons for this terminology will become more apparent when we treat some examples.S的每一个元素称为结果或者样本，在布尔代数B中出现的S的子集称为事件，为什么使用这个术语在我们举例后就会很明显。
第六章 section B 布鲁姆的教育目标分类法 到今天为止，我们可以理直气壮地声称我们的教学目标比较准确地描述了教学所指向的目的。它们在学习和教学中占有重要的作用。 当制定教学目标，提供教学和评价学生成绩时，把存在的不同的标准或学习的结果记在脑中是重要的，把不同标准和结果区分开是重要的，如果教师没有意识到不同的学习的标准，他们很可能专注于一个水平上而忽略其他的。例如，一个教师可能会教大量的事实信息，但从不会抽出时间教学生应用和综合信息，或许一个教师会教更高水平的思考技巧而没有意识到这些技巧必须融入这些更高端技巧的基本技巧的事先学习。 布鲁姆的教育目标分类在认知能力层面上是最著名的，这种分类是等级鲜明的。也就是说，学习者必须先掌握较低层次的目标，在这些目标的基础上通过构建知识达到更高层次的目标，以下是分类的内容： 1、知道（回忆已知的学习知识） 2、领会（把握所学材料的意义） 3、应用（在具体情境中运用知识） 4、分析（把知识分成若干块） 5、综合（把各部分连起来形成整体） 6、评价（按给定的要求通过具体标准评价产品的价值）
知道或知识（回忆信息）代表了布鲁姆分类中的最低层次。它最低是就它最先出现而言的——它为所有高层次的认知活动提供了基础。只有能够对信息进行回忆，学习者才能进入领会这个层次（对信息进行解释）。第三个层次是应用，指的是在新的或者现实情况中运用知识或原理，在这个层次的学习者通过运用前一层次所理解的信息来解决实际问题。第四个层次是分析——将复杂的信息分解成简单的部分，当然，这些简单的部分已经在分类中的前几个层次中得到了解。第五个层次是综合，包括通过整合低层次中的了解到的信息创造出以前不存在的东西。评价是布鲁姆教育目标等级中的最高层次，包括做出一些判断，这些判断基于前几个层次所学习到的根据指定的标准比较某种产品。 这种分类方法的主要价值可以分为两层意思： （1）它可以激发教师帮助学生获得各种不同层次的技能，通过首先确保掌握较低层次的目标来为掌握较高层次的目标铺设适当的基础。 （2）它为发展评价学生各层次学习绩效的测量策略提供了一个基础。 Section C 杰罗姆·布鲁纳的发现学习理论什么是发现学习? 发现学习是一种以质疑为基础的建构主义的学习理论，这种学习发生在问题求解的情况中，在这种情况下，学习者利用他或她过去的经验和现存的知识去探索将要学习的事实和新真理。学生通过探索和
翻译概述（1） 一、学科特点 翻译是一种跨越时空的语言活动，是"把一种语言已经表达出来的东西用另一种语言准确而完整地重新表达出来"(范存忠："漫谈翻译"《翻译理论与技巧》中国对外翻译出版公司，1985，p.80), 是"从语义到文体在译入语中用最切近而又最自然的对等语再现原语的信息"（谭载喜：《奈达论翻译》中国对外翻译出版公司，1984，p.10）。翻译虽为个体所承作，却是一种社会活动，一门综合性很强的学科。它既有很强的理论性又有丰富的实践内涵。就前者而言，翻译经过千百年来各国翻译家的共同努力，已经在语言学、文学、文化、心理学、人类学、哲学和教育学等学科的基础上初步建立了一套理论体系，并在具体实践中总结出了一套行之有效的跨文化和语言转换模式。随着科学的日益进步，这种体系和模式正处在不断地完善之中。就后者而言，翻译是人类社会活动的产物，具有很强的实践性。翻译理论与实践的关系是辨证的；翻译理论产生于翻译实践，反过来又指导实践，实践转过来又丰富翻译理论。可以说，没有社会实践就不会有翻译理论的产生；没有翻译理论作为指导，翻译实践就会难免走弯路。因此，学好翻译既要重视翻译理论的学习，又要加强翻译实践；理论联系实际，这是我们学好翻译的必由之路。 二、为什么可能有翻译 翻译是人类社会发展和进步的需要，因为人类社会要发展进步就需要在不同文化的民族之间进行沟通，而这一全过程都离不开翻译。正如Steiner和张培基所说的那样：Translating it is that openeth the window, to let in the light; that breaketh the shell, that we may eat the kernel. (Steiner) 翻译是沟通各族人民的思想，促进政治、经济、文化、科学、技术交流的重要手段，
Professional English for Industrial Engineering Chapter1 Unit3翻译 姓名： 专业：工业工程 班级： 学号： 完成日期：2015-10-31
Chapter 1 Unit 3 Academic Disciplines of Industrial Engineering 五大主要工程学科和它们的发展 在美国，有五个主要工程学科（土木、化学、电工、工业、机械），它们是早在第一次世界大战时就出现的工程分支学科。这些进步是世界范围内发生的工业革命的一部分，并且在技术革命的开始阶段仍在发生。 随着第二次世界大战的发展导致了其他工程学科的发展，比如核工程，电子工程，航空工程，甚至是电脑工程。太空时代导致了航空工程的发展。最近对环境的关注使得环境工程和生态工程也得到了发展。这些更新的工程学科经常被认为是专长学科包含“五大”学科，即土木，化学，电工，工业，和机械工程里的一种或多种。 和美国的情况不同，工业工程在中国属于第一层级管理科学和工程学科下面的第二级别的学科。 IE学科的开端 学科后来演变成工业工程学科是最初在机械工程系被作为特殊课程教的。首个工业工程的分部在1908年的宾夕法尼亚州大学和雪城大学被建立。（在宾夕法尼亚州的项目是短期存在的，但是它在1925年又重建了）一个在普渡大学的机械工程的IE选科在1911年被建立。一个更完整的工业工程学院项目的历史可能在资料中被找到。 在机械工程部有一个IE选科的实践是主要的模式直到第二次世界大战的结束，并且分离出来的IE部在整个上个世纪里的文理学院和综合大学里被建立。 早在第二次世界大战的时候，在工业工程方面，只有很少的毕业生水平的研究。一旦分开的学部建立之后，学士和博士级别的项目开始出现。 现代IE的教育—分支学科 今天，与过去相比，工业工程对于不同的人来说意味着不同的东西。实际上，一个发展一个突出的现代工业工程的方法是通过获得在它的分支学科和它怎么联系到其他领域的理解。如果在分支学科和工业工程相关联的领域之间有清楚的
中国教育在线考研频道提供考研全方面信息指导及咨询服务，为您成功考研提供一切帮助。 哲学Philosophy 马克思主义哲学Philosophy of Marxism 中国哲学Chinese Philosophy 外国哲学Foreign Philosophies 逻辑学Logic 伦理学Ethics 美学Aesthetics 宗教学Science of Religion 科学技术哲学Philosophy of Science and Technology 经济学Economics 理论经济学Theoretical Economics 政治经济学Political Economy 经济思想史History of Economic Thought 经济史History of Economic 西方经济学Western Economics 世界经济World Economics 人口、资源与环境经济学Population, Resources and Environmental Economics 应用经济学Applied Economics 国民经济学National Economics 区域经济学Regional Economics 财政学（含税收学）Public Finance (including Taxation) 金融学（含保险学）Finance (including Insurance) 产业经济学Industrial Economics 国际贸易学International Trade 劳动经济学Labor Economics 统计学Statistics 数量经济学Quantitative Economics 中文学科、专业名称英文学科、专业名称 国防经济学National Defense Economics 法学Law 法学Science of Law 法学理论Jurisprudence 法律史Legal History 宪法学与行政法学Constitutional Law and Administrative Law 刑法学Criminal Jurisprudence
PPT: 第二页： When you have already acquired a good ability in translation, it’s important for you to storage professional knowledge in mind as more as possible. 1.In financial field: when it comes to 供给and 需求，we say supply and demand in stead of provision and need。 第三页 2.After this week’s disappointing economic figures, China’s central bank said Saturday that it would reduce the share of deposits banks must set aside as reserves. If you have some specific professional knowledge, you know what does“the share of deposits banks must set aside as reserves”mean the moment you see the expression. It means“存款准备金”which is given to the central bank by commercial bank. 3.. The financial futures and options markets which now encircle the globe have risk as their keynote. How to translate “financial futures”and “options markets”？ It means “期货”and “期权”。So it can be translated into“金融期货与期权是目前全球范围内最具冒险性的金融衍生产品”。 第四页：with the development of science and technology , more and more materials concerning science and technology are required to be translated, which puts a high demand on us translators. 1. For example, in scientific and technological area: bedplate has a lot of meanings,such as“底座”、“机座”、“座板”、“底板” 在Cylinder block and bedplate are made of cast-iron．(气缸体和底座均由铸铁制成)句中，we translate “bedplate”to“底座”，it is because in diesel engine，“bedplate”means“底座”或“机座”，not“底板”。However,this sentence: The frame may or may not be provided with a bedplate．(机座可连同底板供应，也可不带底板)，“bedplate”should be translated into “底板”，because底板is a part of electrical machine. 2. In scientific English, different words may have the same meaning. In radio technology, vacuum tube，electron tube名称不同，实际上是同一件东西，如果不知道这一点，而是分别译为“真空管”和“电子管”，译文势必引起混乱。又如比较常见的“AC generator”和“ahemator”都指交流发电机。
翻译是把一种语言里已经表达出来的事物用另一种语言准确流畅地进行重新表达的过程。与其他题材的文章相比,科技专业文章在内容、表达形式和风格上有很大的差别,具有科技性强、专业性强、逻辑严密、表达要求简练的特点,在翻译上力求准确全面、严谨明确和通顺简练。 1科技英语翻译遵循的基本原则 从科技文章的特点来看,大多具有以下几个特征:述说事理、逻辑性强、结构严密、术语繁多,语言严谨、数据精确。这就要求译文必须概念清楚、条理分明、逻辑正确、数据无误,尤其对定义、定律、公式、图表、结论等更应特别注意。科技英语作为特殊英语的一个分支,在词汇构成、遣词造句等方面都有其自身的特点,其语法结构不十分严密、语言习惯和汉语也有不少差别、词汇量大、词语繁多,因此科技英语翻译起来比较困难。另外,科技文章比较重视叙事逻辑上的连贯及表达上的明晰与畅达; 避免行文晦涩,避免表露个人感情,避免论证上的主观随意性。因此,科技英语翻译力求少用或不用描述性形容词以及具有抒情作用的副词、感叹词及疑问词,而是大量使用科技词汇、专业技术用语,译者应尊重客观事实,不能随意改动数据、回避不易翻译的文字,更不能加进自己的主观想象,进行自由翻译。 我国著名翻译家严复提出的“信、达、雅”三准则一直为不少翻译工作者所接受。 “信”指的是译文要忠实于原文,“达”是指译文的通顺达意,“雅”指的是译文的用词修辞。三准则体现了译文和原文信息等值这一基本要领。 “信、达、雅”的翻译准则对各种英语文体的翻译实践都具有指导意义,是衡量一篇译文好坏的标准,也同样适用于科技文献的翻译。由于科技文章特有的文体特征,与其他类文章相比,其“达”和“雅”的内涵不同,它要求在准确传达信息的基础上,使译文更加简洁明快,流畅通顺。2科技英语翻译的基本方法
小议科技英语翻译技巧 科技文体崇尚严谨周密，概念准确，逻辑性强，行文简练，重点突出，句式严整，少有变化，常用前置性陈述，即在句中将主要信息尽量前置，通过主语传递主要信息。科技文章文体的特点是：清晰、准确、精练、严密。那末，科技文章的语言结构特色在翻译过程中如何处理，这是进行英汉科技翻译时需要探讨的问题。现分述如下： 一、大量使用名词化结构 大量使用名词化结构（Nominalization）是科技英语的特点之一。因为科技文体要求行文简洁、表达客观、内容确切、信息量大、强调存在的事实。而非某一行为。 Archimedes first discovered the principle of displacement of water by solid bodies. 阿基米德最先发展固体排水的原理。 句中of displacement of water by solid bodies 系名词化结构，一方面简化了同位语从句，另一方强调displacement 这一事实。 The rotation of the earth on its own axis causes the change from day to night. 地球绕轴自转，引起昼夜的变化。 名词化结构the rotation of the earth on its own axis 使复合句简化成简单句，而且使表达的概念更加确切严密。 If you use firebricks round the walls of the boiler, the heat loss, can be considerably reduced. 炉壁采用耐火砖可大大降低热耗。 科技英语所表述的是客观规律，因之要尽量避免使用第一、二人称；此外，要使主要的信息置于句首。 Television is the transmission and reception of images of moving objects by radio waves. 电视通过无线电波发射和接受活动物体的图象。 名词化结构the transmission and reception of images of moving objects by radio waves 强调客观事实，而"谓语动词则着重其发射和接受的能力。 二、广泛使用被动语句 根据英国利兹大学John Swales 的统计，科技英语中的谓语至少三分之一是被动态。这是因为科技文章侧重叙事推理，强调客观准确。第一、二人称使用过多，会造成主观臆断的印象。因此尽量使用第三人称叙述，采用被动语态，例如：Attention must be paid to the working temperature of the machine.应当注意机器的工作温度。而很少说：You must pay attention to the working temperature of the machine .你们必须注意机器的工作温度。此外，如前所述，科技文章将主要信息前置，放在主语部份。这也是广泛使用被动态的主要原因。试观察并比较下列两段短文的主语。 We can store electrical energy in two metal plates separated by an insulating medium. We call such a device a capacitor, or a condenser, and its ability to store electrical energy capacitance .It is measured in farads. 电能可储存在由一绝缘介质隔开的两块金属极板内。这样的装置称之为电容器，
《工业工程专业英语》 课文翻译 专业：工业工程 学号：11208401 姓名： 指导教师：赵，， 2014年12月
4.2 ERP系统的发展过程 现在，ERP系统无处不在，不仅应用在大型业务中，目前还由运营商们改良后应用在中小企业中。我们需要通过理解ERP系统及其当前体系结构的历史和发展来说明其发展变迁的成果。ERP的优点和缺点会影响它对市场的渗透，系统供应商已经为ERP的推动做好了市场定位和总体策略方面的准备。ERP系统在新的世纪中的应用和发展将依赖于其对客户关系管理、供应链管理一起其他拓展功能的扩充，还有与网络应用的结合。 简介 由微电子、电脑硬件和软件系统驱动的信息和交流的前所未有的增长影响了各种组织的电脑应用的方方面面。同时，公司环境与职能部门日益结合，需要为决策提供越来越多的内部功能数据流，包括及时有效的产品部件的供给、库存管理、清算账目、人力资源以及产品和服务分配等。在这样的条件下，组织管理者需要一个有效的信息系统来降低成本并优化物流，从而提高竞争力。无论是大企业还是中小企业，大家一致认为在复杂的全球化竞争中，及时获得正确的信息的能力能够给企业带来巨大的回报。 从19世纪80年代末到90年代初开始的新的软件系统作为企业资源规划应用在复杂的大型商业企业中从而在工业界中被人们所周知。这种复杂而昂贵，强力而专有的系统供不应求，而且需要根据企业的需求量身定制。很多情况下，ERP实施人员要企业重新设计他们的商业流程来调节软件模型中的物流，从而得到整个企业的数据流。与旧的、传统的自我内部设计的企业专门系统不同，这种软件解决方案结合了多种模型的商业附加包，在需要的时候可以作为附件添加到系统中或者从中删除。 电脑性能的显著提高以及网络给ERP的供应商和设计者们带来的前所未有的挑战，打破了企业与客户定制的隔阂，还包含超出企业内部网络的合作，外部系统需要通过网络来无缝连接。供应商已经许诺了许多的附加功能包，他们中的一些人已经在市场上表现出对这些挑战的接受态度。将产品不断再设计以及在ERP市场中推出新产品和方案是一个永不终止的过程。ERP运营商和客户以及认识到了将其附件按照开放的原则设计，提供可互换的模型，以及容许更简单的定制和客户交流的必要性。 ERP系统定义 企业资源规划系统或企业系统是业务管理软件系统目前，包括模块配套功能区，如计划，制造，销售，市场营销，分销，会计，金融，人力资源管理，项目管理，库存管理，服务，维修，运输和电子商务，架构软件便于模块的透明集成，提供企业内的所有功能之间信息。在运输和电子商务。该架构软件便于模块的透明集成，提供数据流包括良好的企业内的所有功能之间的信息以及与合作公司与通过更换或重新设计实现一个单一的集成系统，其大多是不兼容的传统信息系统。美国生产与库存管理协会（2001）这样定义了ERP系统：“针对物资资源管理、人力资源管理、财务资源管理、信息资源管理集成一体化的企业管理软件。”我们从出版物中摘录了几种定义来更好的解释这个概念：“ERP包含了一个商业软件包，它可以通过企业的财务、清算、人力资源、供应链和客户信息来使数据流无缝结合”（Davenport，1998）。“ERP是将一个组织中的财务和其他信息以及基于信息的流程整合在一起的信息配置系统。”（K&VH,2000）。“一个数据库、一个应用和一个贯穿整个企业的统一界面”（Tadjer，1998）。“ERP系统是为了运作一个组织的业务方便的集成和实时计划、生产，以及客户反馈而设计的基于电脑的系统（OLeary，2001）”。 ERP系统的发展
第十九章 sectionA survey methods survey rearch is the method of gathering data from respondents thought to be representative of some population,using an instrument composed of closed structure or open-ended items (questions). this is perhaps the dominant from of data collection in the social sciences,providing for efficient collection of data over broad populations,amenable to administration in person,by telephone,amd over the internet. some forms of survey research by telephone or the interent may be completely automated. Key terms and concepts the survey instrument is name given to the schedule of question or respone items to be posed to respondents.it is equivalent to the terms questionnaire or interview schedule,depending on the type of survey research being conducted. interviews and questionnaires ordinarily,interviews refers to the face-to-face administration of a survey instrument,whereas quwstionnaires refers to mail or other indirect methods of administration. items are the individual survey question or statements for which a response is solicited from the respondent. Data Collection Modes 1.Face-to-face interviewing is usually the most expensive but it can obtain the highest response rate because it maximizes engagement with the respondent and imposes the lowest burden on the respondent.For the same reasons,face-to-face interviews can support longer instruments.It is also the best data collection type for open-ended responses. 2.Mail surveys are usually among the least expensive modes,are often best for sensitive items, and there is no interviewer bias.However,mail surveys are a poor choice for open-ended items or complex survey designs as they place a high burden on the respondent. 3.Telephone interviewing has the advantage of speed of data collection while supporting longer instruments than mail surveys and supporting open-ended responses,though not as well as face-to-face interviewing. 4.Web surveys are often the least expensive to administer yet can be fast of data collection,particularly since implementation time may be low.Web surveys can be administered to very large populations,even internally. 调查研究的方法是收集数据从受访者认为是代表 一些人口,使用一个仪器由封闭的结构或开放式项目(的问题)。 这也许是最主要的数据收集在社会科学中,提供有效的数据收集在广泛的人群,服从政府的人,通过电话,amd在因特网上。 某些形式的调查研究通过电话或网络营销可能完全自动化。 关键术语和概念 这项调查仪器的名字给了时间表的问题或响应项目对受访者。它与术语问卷或面试时间表,根据类型的调查研究正在进行。 访谈和问卷调查 通常,面试指的是政府的一个测量工具面对面,而问卷指邮件或其他间接的方法管理。 项目是个体调查问题或声明的反应是请求从被申请人。 数据收集方式 1。面对面的面试通常是最昂贵的,但它可以获得最高的响应速度,因为它最大限度地参与被申请人和征收最低被申请人负担。出于同样的原因,面对面的访谈可以支持更长时间的工具。它也是最好的数据集合类型的响应。 2。邮件调查通常是最昂贵的模式,通常最适合敏感物项,没有面试官偏见。然而,邮件调查是一个贫穷的首选项或复杂的调查设计开放式作为他们的地方一个高负担被申请人。 3。电话面试的优点是速度的数据收集工具同时支持长比邮件调查和支持开放式的反应,尽管不是以及面对面的面试。 4。网络调查往往最昂贵的管理还可以快速的数据收集,尤其是实现时间可能较低。网络调查可以被输送到非常大的人口,即使在内部。 SectionB The experimental method is usually taken to be the most scientific of all methods,the "method of choice". The main problem with all the non-experimental methods is lack of control over the situation.The experiment is sometimes described as the cornerstone of psychology:This is partly due to the central role experiments play in many of the physical sciences and also to psychology's historical view of itself as a science.A many of the physical sciences and also to psychological research uses the experimental method. An experiment is a study of one cause and effect.It differs from non-experimental methods in that it involves the deliberate manipulation of one variable,while trying to keep all other variables constant. Experiments in the Laboratory:
翻译基础知识 一、翻译的分类 1.按所涉及的两种代码的性质，可分为语内翻译（intralingual translation）、语际翻译（interlingual translation）、语符翻译（inersemiotic translation）。 2.按翻译主体的性质，可分为人工翻译、机器翻译（Machine Translation）两类。 3.按翻译的工具和成品形式，可分为口译和笔译。 4.按翻译的客体，亦即所译资料的性质，可分为文学翻译（literal translation）和实用翻译（pragmatic translation）。 二、译家译论 1.支谦：在三国时期，支谦的《法句经序》中提出了“因循本旨，不加文饰”的译经原则。 2.道安：晋、前秦时道安在《革卑婆沙序》中提出，“案本而传，不令有损言游字；时改倒句， 余尽实录。”道安涉及译论的佛经序文较多，最有名的是提出“五失本”、“三不易”之说。其意思是，翻译佛经在五种情况下会失去本来面目，有三件事决定了译事是很不容易的，因此必须慎之又慎。 3.彦琮：北朝末年及隋初，彦琮著《辨证论》，它可以看作是我国第一篇翻译专论，他主张译经 “宁贵朴而近理，不用巧而背源”。可见他是坚持忠实第一并倾向于直译的。 4.玄奘：唐代僧人玄奘的指导原则是：“既须求真，又须喻俗”。“求真”即追求准确，要力求“忠 实原作”，这是一切认真负责的翻译工作者的共同理想。同时必须“喻俗”，亦即使群众理解，这就是说要“通顺”。玄奘在译经中成功地运用了补充法、省略法、变位法、分合法、译名假借法、代词还原法等等翻译技巧。 5.马建忠：清末，马建忠在其《马氏文通》中提出“善译”之说：“必先将所译者与所以译者两国之 文字，深嗜笃好，字栉句比，以考彼此文字孳生之源，同异之故。所有当相之实义，委曲推究，务审其声音之高下，析其字句之繁简，尽其文体之变态，及其义理精深奥折之所由然。” 6.林纾：林纾强调在翻译时译者应该投入自己的主观感情，译者须与原作者或作品中人物的心灵 相交流。 7.鲁迅：鲁迅在《且介亭杂文二集》里说：“凡是翻译，必须兼顾着两面，一当然力求其易解，一 则保存着原作得丰姿”。也就是说既要通顺，又要忠实。所谓忠实，是指内容上的“信”；所谓通顺，是指表达上的“顺”。 8.茅盾：文学翻译的目标是“艺术创造性翻译”——用一种语言把原作的艺术意境传达出来，使 读者读译文时能够像读原作时一样得到启发、感动和美的感受。 9.钱钟书：“文学翻译的最高标准是‘化’，把作品从一国文字转变成另一国文字，既不能因语文 习惯的差异而露出生硬牵强的痕迹，又能完全保存原作的风味，那就算得入于‘化境’。十七世纪有人赞美这种造诣的翻译，比为原作的‘投胎转世’，躯壳换了一个，而精神姿致依然故我。换句话说，译本对原作应该忠实得以至于读起来不像译本，因为作品在原文里决不会读起来像经过翻译似的。” 10.傅雷：“以效果而论，翻译应当像临画一样，所求的不在形似而在神似。”“两国文字词类的不 同，句法构造的不同，文法与习惯的不同，修辞格律的不同，俗语的不同，即反映民族思想方式的不同，感觉深浅的不同，观点角度的不同，风俗传统信仰的不同，社会背景的不同，表现方法的不同。以甲国文字传达乙国文字所包含的那些特点，必须像伯乐相马，要“得其精而忘其粗，在其内而忘其外”。而即使最优秀的译文，其韵味较之原文仍不免过或不及。翻译时只能尽量缩短这个距离，过则求其勿太过，不及则求其勿过于不及。”
第一章 IE中的角色 工业工程是新兴的经典和新颖的将计算解决复杂和系统性的问题，在今天的高度科技世界职业之一。，特别是在中国快速发展的经济和其作为世界制造业中心的演技，为IE浏览器的需求将增加，并不断扩大和迫切。 生产系统或服务系统，包括输入，转换和输出。通过改造，增加值的增加，系统的效率和效益都有所提高。转化过程中所使用的技术和管理科学以及它们的组合依靠。 管理生产系统的服务体系，是一个具有挑战性和复杂的，行为科学，计算机和信息科学，经济，以及大量的主题有关的基本原则和技术，生产和服务系统的技术。 对于IE毕业生的需求 工业工程课程设计准备的学生，以满足未来中国的经济和和谐社会建设的挑战。许多即毕业生（IES），事实上，设计和运行现代制造系统和设施。其他选择从事服务活动，如健康，?ìcare交付，金融，物流，交通，教育，公共管理，或咨询等。 为IE毕业生的需求比较旺盛，每年增长。事实上，对于非法入境者的需求大大超过供给。这种需求/供给不平衡是为IE大于其他任何工程或科学学科，并预计在未来多年存在。因此，over165大学或学院于2006年在中国开设了IE浏览器程序。 教科书的目标 这本教科书的主要目的是引入系统化的理论和先进的技术和方法，工业工程，以及他们的英语表达有关科目。教科书的另一个目的是加强和改进学生，AOS与工业工程专业英语文献的阅读和理解能力。 工程与科学 怎么这两个词，?úindustrial，?ùand，?úengineering，?ùget相结合，形成长期，?úindustrial工程，非盟是什么？工业工程和其他工程学科之间的关系，企业管理，社会科学？为了了解工业工程的作用，在今天，AOS经济和知识为基础的的时代，它是有利于学习，希望在IE的演变历史的发展，有许多半途而废写历史发展的工程。治疗本单位是短暂的，因为我们的利益，在审查工程发展的意义，尤其是作为一个专业工业工程的，更完整的历史参考。工程与科学发展并行，相辅相成的方式，虽然他们是电机始终以同样的速度，而科学是有关基本知识的追求，工程与科学知识的应用关注问题的解决方案，并，?úbetter生活的追求，?ù.Obviously，知识不能被应用，直到它被发现的，一经发现，将很快投入使用，在努力解决问题，工程在新知识的地方，提供反馈，以科学因此，科学和工程工作在手的手。 工程应用 - 工具 虽然“科学”和“工程”各有特色，为不同学科，在某些情况下，?úscientist，非盟和?úengineer，非盟可能是同一个人。这是在更早的时候，尤其是当有很少沟通的基本知识的手段。发现知识的人也把它用。 当然，我们也想到如此出色的成绩，在埃及的金字塔，中国长城，罗马的建设项目，等等，当我们回顾早期的工程成就。这些都涉及一个令人印象深刻的应用程序的基本知识。 正如根本，但是，不作为众所周知的成就。斜面，弓，螺旋状，水车，帆，简单的杠杆，以及许多其他方面的发展都非常希望在工程师，AO努力提供更好的生活。 工程的基础 几乎所有的工程发展到1800年之前与物理现象：如克服摩擦，起重，储存，搬运，构造，紧固后的发展，关注与化学和分子现象：如电力，材料，热加工工艺性能，燃烧，和其他的化学过程。 几乎所有的工程发展的基本原则是在数学方面取得的进展。，准确地测量距离，角度，重量和时间的程序进行了细化，实现了更大的成就。
(一)大学生网络学习情况调查研究 摘要：本文基于大连市部分高校大学生网络学习情况的问卷调查所得数据,从多层次、多角度分析了大学生的网络学习现状与资源建设应用情况,就存在的一些问题提出了建议。 关键词：大学生网络学习调查 College Students' learning situation investigation and study Key words:College student Network Learning Investigation Abstract:This thesis based on Dalian university students learning situation survey data, from the multi-level, multi-angle analysis of universties students' learning situation and resource construction and application situations, raise some suggestions about existing problems. （二）北京地区小学阶段基于手机的移动教育发展与需求研究 摘要：移动教育将成为教育信息化深化发展的新方向,成为深入推进素质教育与课程改革的新的创新载体,对推进我国基础教育改革发展具有重要作用。本文从学生、教师、家长三个角度对小学阶段基于手机的移动教育进行研究,深入分析了基于手机的移动教育发展的阻碍因素与促进因素,进行移动教育需求研究,在此基础上,提出小学阶段基于手机的移动教育发展策略。 关键词：小学移动教育发展需求 The research about development and demand of education based on mobile phone in primary school of BJ Abstract:Mobile education will become the new direction of educational informatization deepen development, be of promoting quality education and curriculum reform in the new carrier of innovation has an important role in promoting China basic educational reform development. This article have a research based on primary atage mobile phone education from the students, teachers, parents of three angles, analysis the obstacle factors and promoting factors about mobile phone's mobile education development deeply, mobile education demand research,on this foundation,put forward primary school stage education development strategy based on mobile phone . Key words:Primary School Mobile Education Development Demand
To strengthen the grass-roots Party branch secretary of the ability to perform their duties to promote agricultural modernization Author: Jiang Qin Abstract: the realization of the modernization of Chinese agriculture, is the Chinese Communist Party has always advocated, but also the historical responsibility of the Party branch secretary. Security of China's agricultural modernization to promote better and faster, improve the grass-roots Party branch secretary duties ability is particularly important. This paper will analyze the connotation and basic characteristics of agricultural modernization, and the concrete measures to promote agricultural modernization. Key words: grass roots; Party branch secretary; agricultural modernization Text: The key agricultural modernization is an important content of the modernization of, is the foundation of the modernization, but also solve the problems of Chinese farmers. With the continuous development of our country's economic level, the speed of the modernization process, China's agriculture is facing a new situation and new tasks. Strengthen basic level Party branch secretary of the ability to perform their duties, to solve the problem of agriculture, rural areas and farmers, the agriculture as the most important work of the whole Party and speed up the process of building a new socialist countryside, promoting agricultural modernization. The connotation and characteristics of agricultural modernization. (a) the connotation of agricultural modernization. Refers to the modernization of agriculture from traditional agriculture to modern agriculture transformation process, is the unity of modern intensive agriculture and high commodity agriculture development process. People's understanding of agricultural modernization is different, and it forms a broad and narrow understanding of agricultural modernization. Agricultural modernization in the narrow sense refers only to the changes in the agricultural production technology, and the generalized agricultural modernization includes the coordination of the relationship between the workers and peasants and the modernization of the agricultural economic system and management organization. Correctly understand the connotation of modern agriculture, strengthen basic level Party branch