## 希臘字母

$$

\delta,\lambda\\

\Delta,\Lambda\\

\Alpha\Beta\\

\phi,\varphi\\

\epsilon,\varepsilon\\

π

$$

希臘字母一覽表

## 上下標

$$

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}

$$

## 分式與根式

$$

\frac{1}{2},\frac 1 2\\

\frac{1}{x+y}\\

\frac{\frac{1}{x}+1}{y+1},\frac{\dfrac{1}{x}+1}{y+1}

$$

$$

\sqrt{2},\sqrt{x+y},\sqrt[3]{x}\\

$$

## 普通運算符

$$

+-\\

\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,\R,\Q,\N,\Z,\Z_+\\

\mathcal F,\mathscr F

$$

$$

\cdots,\vdots,\ddots

$$

$$

\infty,\partial,?,\nabla,\propto,\degree

$$

$$

\sin x,\sec x,\cosh x\\

\log_2 x, \ln x,\lg x\\

\lim_{x \to 0} \frac{x}{\sin x}\,\lim\limits_{x \to 0} \frac{x}{\sin x}\\

\max x

$$

$$

MSE(x)錯誤示例,應使用直立體\\

\text{MSE}(x)

$$

## 大型運算符

$$

\sum,\prod\\

\sum_i,\sum_{i=0}^N\\

\frac{\sum_{i=1}^n x_i}{\prod_{i=1}^n x_i}\\

\frac{\sum\limits_{i=1}^n x_i}{\prod\limits_{i=1}^n x_i}\

$$

$$

\int,\iint,\iiint,\oint,\oiint\\

\int_{-\infty}^0 f(x)\,\text d x

$$

$$

a\, a\\

a\ a\\

a\quad a\\

a\qquad a

$$

?## 標注符號

$$

\vec x,\overrightarrow {AB}\\\

\bar x,\overline{AB}

$$

## 箭頭

$$

\leftarrow,\Rightarrow,\Leftrightarrow,\longleftarrow

$$

## 括號和定界符

$$

([])\{\}\\

\lceil,\rceil,\lfloor,\rfloor,||\\?

(0,\frac 1 a],\left(0,\frac 1 a\right]\\

\frac {?f}{?x}|_{x=0},\left.\frac {?f}{?x}\right|_{x=0}

$$

## 多行公式

$$

\begin{align}

a=b+c+d\\ =e+f

\end{align}

$$

$$

\begin{align}

a&=b+c+d\\

&=e+f

\end{align}

$$

## 大括號

$$

f(x)=

\begin{cases}

\sin x, & -π\(zhòng)le x \le π\(zhòng)\

0,& \text{其他}

\end{cases}

$$

## 矩陣

$$

\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}

\begin{pmatrix}

a & b & \cdots & c \\

\vdots& \vdots & \ddots & \vdots \\

e & f& \cdots & g

\end{pmatrix}

\begin{vmatrix}

a & b & \cdots & c \\

\vdots& \vdots & \ddots & \vdots \\

e & f& \cdots & g

\end{vmatrix}

$$

$$

\bf A,\bf B^{\rm T}

$$

## 實戰(zhàn)演練

$$

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\limits_{N\to \infty} P \left\{ \left| \frac {I\left( \alpha_i \right)}{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}

$$