数学专业英语翻译2-6.pptVIP

作业： P57 2: (2),(8) 3: (1) 谢 谢！ New Words Expressions: alphabet 字母表 prime 素数，质数 displacement 位移 proportional 成比例的 domain 定义域 the real-valued function实值函数 edge 棱，边 spring constant 弹性系数 graph 图，图形 limit 极限 stretch 拉伸 volume 体积，容积，卷 2.6 函数的概念与函数思想 Function concept and function idea New Words Expressions(二)P59: admit 准许 mapping 映射 forerunner 先行者 presume 假定 incorporate 并入，结合 trace 追踪 Various fields of human have to do with relationships that exist between one collection of objects and another. 6-A Informal description of functions 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 n1 that cannot be expressed in the