✔ 最佳答案
微積分課程常分為兩個版本: 普通版, ET版
ET即 Early Transcendental的簡稱!
普通版的順序(大約如下):
lim ->代數函數(或加三角函數)的導函數->簡易積分
-> 反函數(指數,對數,反三角函數等, 即越超函數)的導函數與積分
->應用-> 積分方法 ....
ET版的順序(大約如下):
lim -> 所有函數的導函數(含超越函數) ->應用 -> 積分方法 ->...
so, ET版就是將超越函數提前講述(即Early transcendental)!
對學生而言, 普通版比較嚴謹一點, 而ET版比較連貫,但超越函數
部份比較直覺點! 只能說各有千秋, 最好依老師上課指定選書!
OK!?
2009-06-28 13:42:30 補充：
Let A be the ordinary edition, B be the early transcendental edition.
The major difference between A and B is on the discussion of the natural logarithmic function.
Edition A defines ln(x)=∫[0~x] 1/t dt, for x>0, and the Euler's number e is defined by ln(e)=1.
2009-06-28 13:42:40 補充：
This is a theoretical definition of the natural logarithm and the number e.
Edition B defines e=lim(n->∞) (1+1/n)^n, and ln(x)=log_e (x). (logarithm of x with base e)
This is an intuitive definition of ln(x) and e, and is acceptable easily for general students.(my opinions)
