學(xué)堂在線：微積分-1 @陳酌
微積分基本內(nèi)容: 極限論, 函數(shù)微分痴柔、積分理論, 級(jí)數(shù), 場(chǎng)論, 常微分方程 ...
e.g.和i.e.是英語(yǔ)中兩個(gè)容易混淆的拉丁語(yǔ)縮寫:
- 前者是exempli gratia的縮寫诀拭，意思是“for example” (舉例)
- 后者是id est的縮寫，意思是“that is” (即)
Unit 1 Review of Real Numbers (回顧實(shí)數(shù))
§1 Real Numbers (實(shí)數(shù)體系)
術(shù)語(yǔ)：
- R: real numbers (實(shí)數(shù));
- Q: rational numbers (有理數(shù)),
numbers that can be expressed as a/b,
(a over b, called the quotient (商) of a and b),
where a and b are integers and b ≠ 0, - e.g. 2/3 (two-thirds), -5/4 (minus five over four, minus five fourths);
- Z: integers (整數(shù)),
- e.g. -3, -2, -1, 0, 1, 2, ...;
- Z+, +右上標(biāo): nonnegative integers (非負(fù)整數(shù)),
- e.g. 0, 1, 2, ...;
- N: natural numbers (自然數(shù)), also called positive integers (正整數(shù)),
- e.g. 1, 2, 3, 4, ...;
- R\Q=Qc, c右上標(biāo): Irrational numbers (無理數(shù)),
numbers that cannot be expressed as a/b,
where a and b are integers and b ≠ 0, - e.g. 根號(hào)2 (square root of two), pi.
[注] Q 以外的實(shí)數(shù)众辨，用 R backslash Q 表示 Q 的余集
§2 The R2 Plane (R2平面)
R2, 2右上標(biāo).
術(shù)語(yǔ)：
- x-axis (x軸): horizontal axis;
- y-axis (y 軸): vertical axis;
- (x, y): the coordinate (坐標(biāo)) of a point;
- Origin (原點(diǎn)): the point of intersection of two axes, resented by (0, 0).
§3 Operations With Real Numbers (實(shí)數(shù)的基本運(yùn)算)
If a, b, c belong to R, we have:
(a plus parentheses b plus c equals parentheses a plus b plus c)
這個(gè)叫做 單位律. ↑
§4 Inequalities (不等式)
描述兩個(gè)數(shù)大小的時(shí)候, 建立不等式.
§5 Absolute Values of Real Numbers (實(shí)數(shù)的絕對(duì)值)
- |a|: the absolute value (絕對(duì)值) of a.
- Two commonly used inequalities:
(the absolute value of a plus b is always less than or equal to the absolute value of a plus the absolute value of b)
(the absolute value of the difference of the absolute value of a and the absolute value of b is always less than or equal to the absolute value of the difference of a and b)
附錄:
| 運(yùn)算結(jié)果 | 運(yùn)算符 | 運(yùn)算法 |
|---|---|---|
| Sum 和 | plus +, add 加上 | addition 加法 |
| Difference 差 | minus -, subtract 減去 | subtraction 減法 |
| Product 積 | times *, multiplied by 乘以 | multiplication 乘法 |
| Quotient 商 | over /, divided by 除以 | division 除法 |
Unit 1 Summary: 實(shí)數(shù), 運(yùn)算, 兩個(gè)重要的不等式, 英文術(shù)語(yǔ)
Unit 2 Exponentiations, Logarithms and Sets(指數(shù)端三、對(duì)數(shù)與集合)
