数学-纸上得来终觉浅

1. 函数极限的定义($\epsilon,\delta$语言)

2. 函数极限的性质

   1. 唯一性
   2. 局部有界性
   3. 局部保号性

3. 无穷小(let $\alpha$ be infinitesimal)

   1. 性质
      • $\sum\limits_{k}^{N}{\alpha_k}=\alpha,(N \text{ is finite})$
      • $\alpha’\cdot f(x)=\alpha $,where $f(x)$ is limited at the interval
      • $\prod\limits_{k}^{N}{\alpha_k}=\alpha,(N \text{ is finite})$
   2. 比阶($\lim\alpha(x)=0$,$\lim\beta(x)=0$,$\beta(x)\neq0$)
      • $\alpha(x)$是$\beta(x)$的高阶无穷小$\Leftrightarrow\lim{\frac{\alpha(x)}{\beta(x)}}=0$
      • $\alpha(x)$是$\beta(x)$的低阶无穷小$\Leftrightarrow\lim{\frac{\alpha(x)}{\beta(x)}}=\infty$
      • $\alpha(x)$是$\beta(x)$的同阶无穷小$\Leftrightarrow\lim{\frac{\alpha(x)}{\beta(x)}}=c,(\text{constant }c\neq 0)$
      • $\alpha(x)$是$\beta(x)$的等价无穷小$\Leftrightarrow\lim{\frac{\alpha(x)}{\beta(x)}}=1$
      • $\alpha(x)$是$\beta(x)$的$k$阶无穷小$\Leftrightarrow\lim{\frac{\alpha(x)}{\beta^k(x)}}=0$

4. 极限的运算

   1. 四则运算
   2. 洛必达法则
   3. 泰勒展开
   4. 夹逼准则
   5. 七种未定式：$\frac{0}{0},\frac{\infty}{\infty},0\cdot\infty,\infty-\infty,\infty^0,0^0,1^{\infty}$

5. 函数的连续和两类间断点

6. 超实数(hyperreal number)

操作系统-three easy piece

1. cpu-intro
   • the Process
   • Process API
     1. create
     2. Destory
     3. Wait
     4. Miscellaneous Control
     5. Status
   • Process status
   • Proc data structure:(PCB)
2. cpu-api
   1. fork()
   2. wait()
   3. exec()
   4. spawn()*
3. cpu-mechanisms
   1. from Directed Execution to Limited Directed Execution:
      • user mode and kernel mode
      • system call
   2. switch between Processes,Os need to retain CPU from process
      • A Cooperative Approach: Wait For System Calls
      • A Non-Cooperative Approach: The OS Takes Control
      • reboot (x
      • timer interrupt
   3. Saving and Restoring Context
4. cpu-sched(reading)
5. cpu-sched-mlfq(reading)

数据结构-排好队一个一个FIFO

队列

1. 顺序队列的性质和操作
2. 循环队列的性质和操作
3. 链式队列的性质和操作
4. 双端队列

课程编号018-027