math

_posts/2024-03-01-数学学习.md

@@ -138,7 +138,7 @@ $\forall x \exist x$
 
  sin(1/x)有界，有界乘以趋于0的就是0
 
-### mit
+
 
 ![image-20240311105011663](img/2024-03-01-%E6%95%B0%E5%AD%A6%E5%AD%A6%E4%B9%A0/image-20240311105011663.png)
 
@@ -263,7 +263,7 @@ f''(x) = 2c, 1/2 f''(0) = c
 
 ![image-20240717095836968](img/2024-03-01-%E6%95%B0%E5%AD%A6%E5%AD%A6%E4%B9%A0/image-20240717095836968.png)
 
-已知加水速率dV/dt = 2
+### 已知加水速率dV/dt = 2
 
 r/h = 4/10, V = 1/3 πr^2h
 
@@ -277,6 +277,44 @@ dh/dt = 1/2π (升/秒)
 
 ---
 
+### 牛顿迭代法
+
+$x_{n+1} = x_n - \frac {f(x_n)} {f'(x_n)}$ 
+
+![image-20240718104939526](img/2024-03-01-%E6%95%B0%E5%AD%A6%E5%AD%A6%E4%B9%A0/image-20240718104939526.png)
+
+slove x^2 = 5
+
+从x0 = 2开始，f(x) = x^2 - 5, f'(x) = 2x
+
+$x_1 = x_0 - \frac {x_0^2 - 5} { 2x0} = x_0 - 1/2x_0 + 5/2x_0$
+
+x1 = 1/2 * 2 + 5/4 = 9/4
+
+x2 = 1/2 * 9/4 + 5/2 * 4/9 = 161/72
+
+x3 = 1/2 * 161/72 + 5/2 * 161/72
+
+相同写法
+
+slove (64.1)^(1/3) ~= ?
+
+y = x^1/3, dy = 1/3^(-2/3) dx
+
+A + x = 64, y = 64^(1/3) = 4
+
+dy = 1/3(64)^(-2/3) dx = 1/3 * 1/16 dx = 1/48 dx
+
+dx = 1/10, dy = 1/48 dx = 1/480
+
+64.1^(1/3) ~= y + dy = 4 + 1/480
+
+---
+
+### $G(x) = \int g(x)dx $
+
+
+
 
 
 ## 二、线性代数