普林斯顿微积分读本 IV

Mon, 03 May 2021 00:00:00 +0000

§积分

求和符号 —— sigma notation

In general, the number of integers between $A$ and $B$, including $A$ and $B$, is $B - A + 1$.

注意：$\sum\limits_{A}^{B}$ 共有 $B-A+1$ 个数求和

$$ S = \sum_{i=1}^{100}i = \sum_{i=1}^{100}(101-i) $$

$2S = \sum_{i=1}^{100}(i+101-i) = \sum\limits_{i=1}^{100}101$

伸缩级数（telescoping series）

$$ \sum_{j=a}^{b}(f(j)-f(j-1))=f(b)-f(a-1) $$

$$ mesh=max(t_1 - t_0); (t_2 - t_1); ... ; (t{n-1} - t{n-2}); (t_n - t_{n-1}) $$

Riemann sum（黎曼和）：速度曲线下的实际面积