continuous

Fixed point iteration

這裡我們介紹固定點迭代法 (Fixed point iteration) 首先我們介紹什麼是固定點 (Fixed point) Definition: Fixed point A fixed point of a function $f(x)$ is a number $c$ in its domain such that $f(c)=c$. 所以簡單來說, 把固定點這個數字丟進函數後會

Maximum and minimum of a function

這裡我們要討論一個函數的最大值以及最小值. 首先我們有極值定理 Theorem: Extreme value theorem If $f$ is a real-valued continuous function on the closed interval $[a,b]$, then $f$ must attain a maximum and a minimum. 所以對於定義在封閉區間的連續函