數(shù)學(xué)專業(yè)外語第三講

1、Key points: useful terms and definitions of Mathematics, equation and geometryDifficult points: Some geometrical terms,New Words & Expressions:geometry n. 幾何學(xué)function theory 函數(shù)論 trigonometry n. 三角

2、學(xué)conception n. 概念algebra n. 代數(shù)學(xué)proposition 命題equation 方程,等式definition 定義constant n. 常量notation 符號, 記號mathematical analysis 數(shù)學(xué)分析 logical deduction 邏輯推理, 推論Roman-number n. 羅馬數(shù)字,2.1 數(shù)

3、學(xué)、方程與比例Mathematics, Equation and Ratio,New Words & Expressions:higher mathematics 高等數(shù)學(xué)differential equation 微分方程equation of condition 條件等式 linear equation 線性等式variable adj. 變化的, n.變量

4、dimension 大小,維數(shù),尺寸formula 公式even number 偶數(shù)arithmetic 算術(shù),算術(shù)的numerical 數(shù)值的, 數(shù)字的fraction 分?jǐn)?shù) identity 恒等式 term 項(xiàng), 術(shù)語, 命名為algebraic 代數(shù)的operation 運(yùn)算,Mathematics comes from man’s social practice, for exam

5、ple, 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

6、modern scientific and technological branches could be regularly developed without the application of mathematics.數(shù)學(xué)來源于人類的社會實(shí)踐, 比如工農(nóng)業(yè)生產(chǎn), 商業(yè)活動, 軍事行動和科學(xué)技術(shù)研究. 反過來, 數(shù)學(xué)服務(wù)于實(shí)踐, 并在各個領(lǐng)域中起著非常重要的作用. 沒有應(yīng)用數(shù)學(xué), 任何一個現(xiàn)在的科技的分支都不能正常發(fā)展.,1－

7、A What is mathematics,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 som

8、e more complex practical problems, man established and then solved equation with unknown numbers, thus algebra occurred. 很早的時候, 人類的需要產(chǎn)生了數(shù)和形式的概念. 接著,測量土地的需要形成了幾何，出于測量的需要產(chǎn)生了三角幾何. 為了處理更復(fù)雜的實(shí)際問題，人類建立和解決了帶未知參數(shù)的方程, 從而產(chǎn)生了代數(shù)學(xué).

9、,Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry, trigonometry and algebra, in which only the constants are considered.The rapid development of industry in 17th century promoted

10、the progress of economics and technology and required dealing with variable quantities.17世紀(jì)前, 人類局限于只考慮常數(shù)的初等數(shù)學(xué)，即幾何，三角幾何和代數(shù)。17世紀(jì)工業(yè)的快速發(fā)展推動了經(jīng)濟(jì)技術(shù)的進(jìn)步, 從而遇到需要處理變量的問題。,The leap from constants to variable quantities brought ab

11、out 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, dif

12、ferential equations, function theory and so on.從常數(shù)帶變量的跳躍產(chǎn)生了兩個新的數(shù)學(xué)分支--解析幾何和微積分, 他們都屬于高等數(shù)學(xué).現(xiàn)在高等數(shù)學(xué)里面有很多分支, 其中有數(shù)學(xué)分析, 高等代數(shù), 微分方程, 函數(shù)論等.,Mathematicians study conceptions and propositions. Axioms, postulates, definitions and

13、 theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. 數(shù)學(xué)家研究的是概念和命題, 公理, 公設(shè), 定義和定理都是命題. 符號是數(shù)學(xué)中一個特殊而有用的工具, 常用于表達(dá)概念和命題.

14、,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, div

15、ision and equality.公式, 圖表都是不同的符號. 阿拉伯?dāng)?shù)字1, 2, 3, 4, 5, 6, 7, 8, 9, 0和加, 減, 乘, 除, 等式都是一些常見的符號.,The conclusions in mathematics are obtained mainly by logical deductions and computation. For a long period of the history

16、of mathematics, the centric place of mathematics methods was occupied by the logical deductions. 數(shù)學(xué)結(jié)論主要由邏輯推理和計算得到.在數(shù)學(xué)發(fā)展歷史的很長時間內(nèi), 邏輯推理一直占據(jù)著數(shù)學(xué)方法的中心地位.,Now, since electronic computers are developed promptly and used wide

17、ly, 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 lo

18、gical deductions, for example, the proof of most of geometrical theorems.現(xiàn)在, 由于電子計算機(jī)的迅速發(fā)展和廣泛使用, 計算的地位越來越重要.現(xiàn)在計算機(jī)不僅用于處理大量的信息和數(shù)據(jù), 還可以完成一些之前只能由邏輯推理來做的工作, 例如大多數(shù)幾何定理的證明.,回顧：如果沒有運(yùn)用數(shù)學(xué)， 任何一個科學(xué)技術(shù)分支都不可能正常的發(fā)展 。 No modern s

19、cientific and technological branches could be regularly developed without the application of mathematics.符號是數(shù)學(xué)中一個特殊而有用的工具, 常用于表達(dá)概念和命題. Notations are a special and powerful tool of mathematics and are used to expre

20、ss conceptions and propositions very often.,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 a

21、n algebraic identity is an equation. 等式是關(guān)于兩個數(shù)或者數(shù)的符號相等的一種描述。等式有兩種－恒等式和條件等式。算術(shù)或者代數(shù)恒等式是等式。,1－B Equation,In such an equation either the two members are alike, or become alike on the performance of the indicated operati

22、on.An identity involving letters is true for any set of numerical values of the letters in it.這種等式的兩端要么一樣，要么經(jīng)過執(zhí)行指定的運(yùn)算后變成一樣。含有字母的恒等式對其中字母的任一組數(shù)值都成立。,An equation which is true only for certain values of a letter in it,

23、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 v

24、alues for x and y.一個等式若僅僅對其中一個字母的某些值成立，或?qū)ζ渲袃蓚€或著多個字母的若干組相關(guān)的值成立，則它是一個條件等式，簡稱方程。因此3x-5=7僅當(dāng)x=4 時成立，而2x-y=0，當(dāng)x=6,y=2時成立，且對x, y的其他許多對值也成立。,A root of an equation is any number or number symbol which satisfies the equation.T

25、here are various kinds of equation. They are linear equation, quadratic equation, etc.To solve an equation means to find the value of the unknown term.方程的根是滿足方程的任意數(shù)或者數(shù)的符號。方程有很多種，例如： 線性方程，二次方程等。解方程意味著求未知項(xiàng)的值.,To do th

26、is , 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. We then obtain the value of the unknown and the answe

27、r to the question. 為了求未知項(xiàng)的值，當(dāng)然必須移項(xiàng)，直到未知項(xiàng)單獨(dú)在方程的一邊，令其等于方程的另一邊。從而求得未知項(xiàng)的值，解決了問題。,To solve the equation, therefore, means to move and change the terms about without making the equation untrue, until only the unknown quanti

28、ty is left on one side, no matter which side.Equation are of very great use.We can use equation in many mathematical problems.因此解方程意味著進(jìn)行一系列的移項(xiàng)和同解變形，直到未知量被單獨(dú)留在方程的一邊，無論那一邊。方程作用很大?？梢杂梅匠探鉀Q很多數(shù)學(xué)問題。,We may notice that alm

29、ost 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.注意到幾乎每一個問題都給出一個或多個關(guān)于一個事情與另一個事情相等的陳述，這就給出了方程，利用該方程，如果我們需要的話，可以解方程。,精品

30、課件！,精品課件！,回顧：一個等式若僅僅對其中一個字母的某些值成立，或?qū)ζ渲袃蓚€或著多個字母的若干組相關(guān)的值成立，則它是一個條件等式，簡稱方程。 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