$$\begin{alignedat}{2}10&x+ &3&y = 2 \\ 3&x+&13&y = 4\end{alignedat}$$

$$\overbrace{a+b+c}^{\text{note}}$$

$$\tag{2.1}A=\overbrace{(a+b)+\underbrace{(c+d)i}_{\text{虚数}}}^{\text{复数}}+(e+f)+\underline{(g+h)}$$

$$\tag{2.2}\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$$

$$\tag{2.3}\int_{a}^{b}f(x)dx=F(b)-F(a)$$

$$
\left[
\begin{array}{cc|c}
1&1&1 \\
2&2&2 \\  \hline
3&3&3
\end{array}
\right]
$$

$$
\begin{Vmatrix}
      a5 & b \\
      c & d
\end{Vmatrix}
$$

$$R^2=1-\frac{SS_{res}}{SS_tot}=1-\frac{\sum{(y_i-\hat y_i)^2}}{(y_i-\bar y)^2}$$

$$
\tag{2.4}
\frac{d}{dx}e^{ax}=ae^{ax}\quad\sum_{i=1}^{n}{(X_i - \overline{X})^2}
$$

$$
\begin{aligned}
a_0&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\,\mathrm{d}x\\[6pt]
a_n&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos nx\,\mathrm{d}x=\\
&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\cos nx\,\mathrm{d}x\\[6pt]
b_n&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\sin nx\,\mathrm{d}x=\\
&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}x^2\sin nx\,\mathrm{d}x
\\[6pt]
\end{aligned}
$$

$$
z = \overbrace{
   \underbrace{x}_\text{real} + i
   \underbrace{y}_\text{imaginary}
  }^\text{complex number}
$$

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

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

$$
\left\{
\begin{array}{c}
    a_1x+b_1y+c_1z=d_1 \\
    a_2x+b_2y+c_2z=d_2 \\
    a_3x+b_3y+c_3z=d_3
\end{array}
\right.
$$

$$
h(\theta) = \sum_{j = 0} ^n \theta_j x_j
$$

$$
J(\theta) = \frac{1}{2m}\sum_{i = 0} ^m(y^i - h_\theta (x^i))^2
$$

$$
\frac{\partial J(\theta)}{\partial\theta_j}=-\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j
$$

$$
\begin{aligned}
\frac{\partial J(\theta)}{\partial\theta_j}
& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(y^i-h_\theta(x^i)) \\
& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(\sum_{j=0}^n\theta_jx_j^i-y^i) \\
& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j
\end{aligned}
$$

$$
\begin{gathered}
\operatorname{arg\,max}_a f(a)
= \operatorname*{arg\,max}_b f(b) \\
\operatorname{arg\,min}_c f(c)
= \operatorname*{arg\,min}_d f(d)
\end{gathered}
$$

$$
  \prod_{{
  \begin{gathered}
            1\le i \le n\\
            1\le j \le m
  \end{gathered}
            }}
     M_{i,j}
$$

$$
\sqrt x * \sqrt[3] x * \sqrt[-1] x
$$
$$\dot{\sigma}=\beta*\pi$$

$$
y=x^2 \tag{1.5a} \label{eq:test}
$$

新的测试， 挺好玩的；
$$
\beta=\pi, \eqref{eq:test}
$$

$$
\left\{
    \begin{aligned}     %请使用'aligned'或'align*'
    2x + y &= 1  \\     %加'&'指定对齐位置
    2x + 2y &= 2
    \end{aligned}
    \right.
$$

$$
B \scriptscriptstyle i,n \displaystyle (t)=\dbinom{n}{i} ti(1-t){n-i},i = 0,…,n, \tag{2}
$$

$$
\left[
\begin{matrix}
B_{0,3}(t_0) & \cdots & B_{3,3}(t_0) \\
B_{0,3}(t_1) & \cdots & B_{3,3}(t_1) \\
\vdots & \ddots & \vdots \\
B_{0,3}(t_m) & \cdots & B_{3,3}(t_m)
\end{matrix}
\right]
\left[
\begin{matrix}
b_{x0} & b_{y0} \\
b_{x1} & b_{y1} \\
b_{x2} & b_{y2} \\
b_{x3} & b_{y3}
\end{matrix}
\right] =
\left[
\begin{matrix}
p_{x0} & p_{y0} \\
p_{x1} & p_{y1} \\
\vdots & \vdots \\
p_{xm} & p_{ym}
\end{matrix}
\right]
$$

$$
\bigl(x\in A(n)|x\in B(n)\bigr)$$
$$
\bigl(x\in A(n)\bigm|x\in B(n)\bigr)
$$

$$
\left( \begin{array}{ccc}
x_{11} & x_{12} & \ldots \\
x_{21} & x_{22} & \ldots \\
\vdots & \vdots & \ddots
\end{array} \right)
$$

$\mathbb{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}$

$$\arg\min\limits_{\theta} \ \ \| \mathrm{J} (\theta)\|$$
$$
\mathop{\arg\min}\limits_{\theta} \ \ \| \mathrm{J} (\theta)\|
$$

$$
L(Y,f(x))=
\begin{cases}
1, Y!=f(x) \\
0, Y = f(x)
\end{cases}
$$

$$
\left\{
\begin{aligned}
\frac{d r}{d \omega^{\prime}}&=\frac{v}{f \omega^{\prime}} \\
\frac{d v}{d \omega^{\prime}}&=\frac{(F / m) \sin \psi-g / r^{2}+r_{\omega^{2}}}{f \omega^{\prime}} \\
\frac{\mathrm{d} \theta}{\mathrm{d} \omega^{\prime}}&=\frac{\omega}{f \omega}\\
\frac{\mathrm{d} \omega}{\mathrm{d} \omega^{\prime}}&=-1 \\
\frac{\mathrm{d} m}{\mathrm{d} \omega^{\prime}}&=-\frac{F}{I_{\mathrm{sp}}} \cdot \frac{1}{f \omega^{\prime}}
\end{aligned}
\right.
$$