一个MATLAB 的程序学习

$$
\begin{aligned}
&max=2*x1+3*x2;\\
&\text{s.t.}\\
&x1+2*x2<=8;\\
&4*x1<=16;\\
&s4*x2<=12;
\end{aligned}
$$

$$
f(x)=\int_{2}^{+\infty} \frac{dx}{x\cdot \sqrt[3]{x^2-3x+2}}
$$

$$
\lim_{x\rightarrow{\infty}}(1+\frac{1}{x})^{x}=e
$$
$$
\begin{cases}
   y'' &=f(x,y,y') \\
   y|_{x=x_0}&=y_0 \\
   y'|_{x=x_0}&=y'_0
\end{cases}
$$
$$
\left(h\frac{\partial}{\partial x}  + k\frac{\partial}{\partial y} \right) ^m
f(x_0,y_0)  =\sum_{p=0}^{m}C_m^ph^pk^{m-p}
\frac{\partial^mf}{\partial x^p\partial y^{m-p}}\Big|_{x_0-y_0}
$$

Gamma公式展示 $\Gamma(n) = (n-1)!\quad\forall
n\in\mathbb N$ 是通过欧拉积分
$$
\Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,.
$$

$$A^TA=\left(              
\begin{array}{lcr}   
1 & 2 \\
0 & 0 \\           
0 & 0
\end{array}         
\right)
\left(              
\begin{array}{lcr}   
1 & 0 & 0 \\           
2 & 0 & 0
\end{array}         
\right)=
\left(              
\begin{array}{lcr}   
5 & 0 & 0 \\           
0 & 0 & 0 \\
0 & 0 & 0
\end{array}         
\right)$$，

$$
            \begin{pmatrix}
            1 & a_1 & a_1^2 & \cdots & a_1^n \\
            1 & a_2 & a_2^2 & \cdots & a_2^n \\
            \vdots & \vdots & \vdots & \ddots & \vdots \\
            1 & a_m & a_m^2 & \cdots & a_m^n \\
            \end{pmatrix}
$$

有趣；[backcolor=rgb(238, 238, 238) !important]$ y_k=\varphi(u_k+v_k)$ [backcolor=rgb(238, 238, 238) !important]$J\alpha(x) = \sum{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}^{2m + \alpha}$注意下面的写法：(右对齐)[backcolor=rgb(238, 238, 238) !important]$$ y_k=\varphi(u_k+v_k)$$

$$\frac{\partial u}{\partial t}
= h^2 \left( \frac{\partial^2 u}{\partial x^2}
+ \frac{\partial^2 u}{\partial y^2}  
+ \frac{\partial^2 u}{\partial z^2}\right)$$

$$ F^{HLLC}=\left\{
\begin{array}{rcl}
F_L       &      & {0      <      S_L}\\
F^*_L     &      & {S_L \leq 0 < S_M}\\
F^*_R     &      & {S_M \leq 0 < S_R}\\
F_R       &      & {S_R \leq 0}
\end{array} \right. $$

$$
matrix
\left[ \left( \begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array} \right)\right]$$
$$
\left[ \chi(\lambda) = \left| \begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array} \right|.\right]
$$

$$
f(x) = \left\{
  \begin{array}{lr}
    x^2 & : x < 0\\
    x^3 & : x \ge 0
  \end{array}
\right.
$$

$$
u(x) =
  \begin{cases}
   \exp{x} & \text{if } x \geq 0 \\
   1       & \text{if } x < 0
  \end{cases}
$$