LATEX笔记

希腊字母

$$\begin{gathered} \delta ,\alpha ,\beta \\ \Delta \end{gathered}$$

上下标

$$\begin{gathered} x^2 \\ {x}^{y+1} \\ {y}_1,x_{ij} \end{gathered}$$

分式与根式

$$\begin{gathered} \frac{1}{2},\frac{3}{4} \\ \frac{\frac{1}{x}+1}{y+1} \end{gathered}$$

$$\begin{gathered} \sqrt{2} \\ \sqrt[3]{7x} \end{gathered}$$

普通运算符

$$

• -\
  \times,\cdot,\div\
  \pm,\mp\
  <> \ge,\le,\gg,\ll,\ne,\approx,\equiv\
  \cap,\cup,\in,\notin,\subseteq,\subsetneq,\subsetneqq,\varnothing\
  \forall,\exists,\nexists\
  \because,\therefore\
  \mathbb R,\R,\Q,\N,\Z,\Z_+\
  \mathcal F,\mathscr F
  $$

$$\cdots ,⋮,\ddots$$

$$\infty ,\partial ,\nabla ,\propto ,°$$

$$\begin{gathered} \sin x,\sec x,\cosh x \\ {\log }_{2}x,\ln x,\lg x \\ \underset{x\to 0}{\lim }\frac{x}{\sin x} \\ \max x,\min x \end{gathered}$$

大型运算符

$$\begin{gathered} \sum ,\prod \\ \sum _{i=0}^N \end{gathered}$$

$$\begin{gathered} \int ,\iint ,\iiint ,\oint ,\iint \\ {\int }_0^{\infty }f(x)\text{d}x \end{gathered}$$

$$\begin{gathered} 间距 \\ aa \\ aa \\ aa \\ aa \end{gathered}$$

标注符号

$$\begin{gathered} \vec{x},\overrightarrow{AB} \\ \bar{x},\overline{AB} \end{gathered}$$

箭头

$$\begin{gathered} \leftarrow ,\to ,\leftrightarrow \\ \Leftarrow ,\Rightarrow ,\iff \end{gathered}$$

括号与定界符

$$
()[] {}大括号被LATEX占用了\
\lceil , \rceil,\lfloor,\rfloor\
\left(1,2\right]\

$$

多行公式

$$
\begin{align}
a&=b+c\
&=e+f\

\end{align}
$$

$$
\begin{align}

P_{DOUT}^{D}&=P\left[ \min \left{ \log \left( 1+\gamma _{T,R} \right) ,\log \left( 1+\gamma _{R,D} \right) \right} <R \right] \\ &=P\left[ \min \left{ \gamma _{T,R},\gamma _{R,D} \right} <2^R-1 \right]

\end{align}
$$

大括号

$$
f(x)=
\begin{cases}
sin x,&0<x \le6\
cos x,&6<x<100\
0,&\text(其他)

\end{cases}
$$

矩阵

$$
\begin{matrix}
a & b & \cdots & c\
d & e & \cdots & f\
\vdots & \vdots & \ddots&\vdots &\
h & i & \cdots &g &\text{没有括号矩阵}

\end{matrix}
$$

$$
\begin{bmatrix}
a & b & \cdots & c\
d & e & \cdots & f\
\vdots & \vdots & \ddots&\vdots &\
h & i & \cdots &g

\end{bmatrix}\text{方括号矩阵}

\begin{pmatrix}
a & b & \cdots & c\
d & e & \cdots & f\
\vdots & \vdots & \ddots&\vdots &\
h & i & \cdots &g

\end{pmatrix}\text{圆括号矩阵}

\begin{vmatrix}
a & b & \cdots & c\
d & e & \cdots & f\
\vdots & \vdots & \ddots&\vdots &\
h & i & \cdots &g

\end{vmatrix}\text{行列式}
$$

$$\mathbf{A}\text{矩阵A},{\mathbf{B}}^{\mathrm{T}}$$

实战演练

$$f(x)=\frac{1}{\sqrt{2\pi }\sigma }{\mathrm{e}}^{-\frac{(\mathrm{x}-\mu {)}^2}{2{\sigma }^2}}\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{2\pi }\sigma }\exp \left[-\frac{(\mathrm{x}-\mu {)}^2}{2{\sigma }^2}\right]$$

$$\begin{gathered} \underset{N\to \infty }{\lim }P\left\{\left|\frac{I({\alpha }_i)}{N}-H(s)\right|<\epsilon \right\}=1 \\ \underset{x\to 0}{\lim }\frac{x}{\sin x} \end{gathered}$$

$$x(n)=\frac{1}{2\pi }{\int }_{-\pi }^{\pi }X\left({\mathrm{e}}^{\mathrm{j}\omega }\right)e^{j\omega n}\mathrm{d}\omega$$