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| ## 希腊字母
小写字母：
$$
\alpha,\ \beta,\ \gamma,\ \delta,\ \epsilon,\ \zeta,\ \eta,\ \theta,\ \iota,\ \kappa,\ \lambda,\ \mu,\ \nu,\ \xi,\ \omicron,\ \pi,\ \rho,\ \sigma,\ \tau,\ \upsilon,\ \phi,\ \chi,\ \psi,\ \omega
$$
大写字母：
$$
\Gamma,\ \Delta,\ \Theta,\ \Lambda,\ \Xi,\ \Pi,\ \Sigma,\ \Upsilon,\ \Phi,\ \Psi,\ \Omega
$$
常见变体：
$$
\varepsilon,\ \vartheta,\ \varpi,\ \varrho,\ \varsigma,\ \varphi
$$
## 上下标
$$
\begin{array}{cl}
a^2,a_1\\\\
x^{y+z},p_{ij},p_ij\\\\
x_i,x_{\text i}\\\\
\text{A B},\rm{A B}\\\\
\text A B,\rm A B\\\\
{\rm A} B\\\\
\text{e},\text{i}
\end{array}
$$
## 分式与根式
$$
\frac{1}{2},\frac 1 2,\\
\frac 1 {x+y}\\
\frac {\dfrac 1 x + 1}{y + 1}
$$
$$
\sqrt 2,\sqrt{x+y},\sqrt[3]x
$$
## 普通运算符
$$
\begin{array}{cl}
+-\\\\
\times,\cdot,\div\\\\
\pm,\mp\\\\
\ge,\le,\gg,\ll,\ne,\approx,\equiv\\\\
\cap,\cup,\in,\notin,\subseteq,\subsetneqq,\varnothing\\\\
\forall,\exists,\nexists\\\\
\because,\therefore\\\\
\mathbb R,\mathbb R,\mathbb Q,\mathbb N,\mathbb Z_+\\\\
\mathcal F,\mathscr F
\end{array}
$$
$$
\cdots,\vdots,\ddots
$$
$$
\infty,\partial,∂,\nabla,\propto,\degree
$$
$$
\begin{array}{cl}
\sin x,\sec x,\cosh x\\\\
\log_2 x, \ln x,\lg x\\\\
\lim\limits_{x \to 0} \frac { x}{\sin x}\\\\
\max x
\end{array}
$$
$$
\text{MSE}(x)
$$
## 大型运算符
$$
\sum,\prod\\
\sum_i,\sum_{i=0}^N\\
\frac{\sum\limits_{i=1}^n x_i}{\prod\limits_{i=1}^n x_i}
$$
$$
\begin{array}{cl}
\int & \verb|\int| \text{ 单重积分} \\\\
\iint & \verb|\iint| \text{ 二重积分} \\\\
\iiint & \verb|\iiint| \text{ 三重积分} \\\\
\oint & \verb|\oint| \text{ 曲线积分} \\\\
\unicode{x222F} & \verb|\unicode{x222F}| \text{ 曲面积分 (oiint)} \\\\
\unicode{x2230} & \verb|\unicode{x2230}| \text{ 三重曲面积分 (oiiint)}
\end{array}
$$
$$
\int_{-\infty}^0 f(x)\,\text d x\\
$$
$$
\begin{array}{cl}
a\, a \\\\
a\ a \\\\
a\quad a \\\\
a\qquad a
\end{array}
$$
## 标注符号
$$
\vec x,\overrightarrow {AB}\\
\bar x,\overline{AB}
$$
## 箭头
$$
\leftarrow,\Rightarrow,\Leftrightarrow,\longleftarrow
$$
## 括号与定界符
$$
\begin{array}{cl}
([])\{ \}\\\\
\lceil,\rceil,\lfloor,\rfloor,||\\\\
\left(0,\frac 1 a\right]\\\\
\left.\frac {∂f}{∂x}\right|_{x=0}
\end{array}
$$
## 多行公式
$$
\begin{align} a&=b+c+d\\\\
\&=e+f \end{align}
$$
## 大括号
$$
f(x)=
\begin{cases}
\sin x, & -π\le x \le π\\\\
0,& \text{其他}
\end{cases}
$$
## 矩阵
$$
\begin{matrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{matrix}
$$
$$
\begin{bmatrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{bmatrix}
\quad
\begin{pmatrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{pmatrix}
\quad
\begin{vmatrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{vmatrix}
$$
$$
\begin{Bmatrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{Bmatrix}
\quad
\begin{Vmatrix}
a & b & \cdots & c \\\\
\vdots & \vdots & \ddots & \vdots \\\\
e & f & \cdots & g
\end{Vmatrix}
$$
$$
\bf A,\bf B^{\rm T}
$$
## 实战演练
$$
f(x) = \frac 1 {\sqrt{2\pi} \sigma} {\rm e} ^ {-\frac {(x-\mu)^2}{2\sigma ^ 2}}\\\\
f(x) = \frac 1 {\sqrt{2\pi} \sigma} \exp \left[ {-\frac {(x-\mu)^2}{2\sigma ^ 2}}\right]
$$
$$
\\lim_{N\\to\\infty} P\\left\\{\\left|\\frac{I(\\alpha_i)}{N} - H(s)\\right| < \\varepsilon\\right\\} = 1
$$
$$
x(n) = \frac 1 {2\pi} \int _{-π} ^ π X\left( {\rm e} ^ {{\rm j} \omega } \right) {\rm e} ^ {{\rm j} \omega n} \, {\rm d}\omega\\
$$
$$
\begin{align}
\vec B \left( \vec r \right) &= \frac {\mu_0}{4\pi}\oint_C \frac {I \, {\rm d} \vec l \times \vec R}{R^3}\\\\
&= \frac {\mu_0}{4\pi} \int_V \frac{\vec J_V \times \vec R}{R^3}\, {\rm d} V'
\end{align}
$$
|
