Common LaTeX Formulas

1. Inserting Formulas

Inline Formulas

$f(x)=x$

$f(x)=x$

Display Formulas

$f(x)=x$

$f(x)=x$

2. Math Operators

Multiplication and Division

$a \times b$
$a \div b$

$a \times b$ $a \div b$

Fractions

$\frac{a}{b}$

$\frac{a}{b}$

Square Roots

$\sqrt{}$
$\sqrt[m]{n}$

$\sqrt{3}$ $\sqrt[m]{n}$

Derivatives and Partial Derivatives

$\frac{\mathrm{d}y}{\mathrm{d}x}$ %求导
$\frac{\partial f}{\partial x}$   %偏导
$f^{'}(x)$     %求导撇
$f^{''}(x)$
$\dot{y}$      %求导点
$\ddot{y}$
$\dddot{y}$
$\nabla{f}$    %全微分

$\frac{\mathrm{d}y}{\mathrm{d}x}$

$\frac{\partial f}{\partial x}$

$f^{'}(x)$ $f^{''}(x)$

$\dot{y}$ $\ddot{y}$ $\dddot{y}$

$\nabla{f}$

Absolute Value

$|x_n|$
$\lvert x_n\rvert$

$|x_n|$ $\lvert x_n\rvert$

Summation

$\sum_{i=1}^{n}$

$\sum_{i=1}^{n}$

Product

$\prod_{i=1}^{n}$

$\prod_{i=1}^{n}$

Integration

$\int_{i=1}^{n}$

$\int_{i=1}^{n}$

Matrices

$$
P=\begin{bmatrix}{}
p_{1,1} & p_{1,2} & \cdots & p_{1,|S|}\\
p_{2,1} & p_{2,2} & \cdots & p_{2,|S|}\\
\cdots & \cdots & \cdots & \cdots\\
p_{|S|,1} & p_{|S|,2} & \cdots & p_{|S|,|S|}
\end{bmatrix}
$$

$$P=\begin{bmatrix}{} p_{1,1} & p_{1,2} & \cdots & p_{1,|S|}\\ p_{2,1} & p_{2,2} & \cdots & p_{2,|S|}\\ \cdots & \cdots & \cdots & \cdots\\ p_{|S|,1} & p_{|S|,2} & \cdots & p_{|S|,|S|} \end{bmatrix}$$

3. Letter Modifiers

Subscripts and Superscripts

^{} %上标$x^{2}$
_{} %下标$x_{1}$

$x^{2}$ $x_{1}$

Vectors

$\vec{a}$
$\overrightarrow{AB}$

$\vec{a}$ $\overrightarrow{AB}$

Ellipsis

$\cdots$   %省略号...$1,2,3,\cdots,n$

$1,2,3,\cdots,n$

Braces

$\underbrace{n}_{m}$ % 大括号 \underbrace{1,2,3,\cdots,n}_{m}

$\underbrace{1,2,3,\cdots,n}_{m}$

Overline and Underline

$\overline{m+n}$ %m+n公式上面加上横杠 
$\underline{m+n}$%m+n公式下面加上横杠

$\overline{m+n}$

$\underline{m+n}$

4. Special Letters

Greek Alphabet

Lowercase Greek	Code	Uppercase Greek	Code
$\alpha$	\alpha
$\beta$	\beta
$\gamma$	\gamma	$\Gamma$	\Gamma
$\delta$	\delta	$\Delta$	\Delta
$\epsilon$	\epsilon
$\varepsilon$	\varepsilon
$\zeta$	\zeta
$\eta$	\eta
$\theta$	\theta	$\Theta$	\Theta
$\vartheta$	\vartheta
$\iota$	\iota
$\kappa$	\kappa
$\lambda$	\lambda	$\Lambda$	\Lambda
$\mu$	\mu
$\nu$	\nu
$\xi$	\xi	$\Xi$	\Xi
$\pi$	\pi	$\Pi$	\Pi
$\varpi$	\varpi
$\rho$	\rho
$\varrho$	\varrho
$\sigma$	\sigma	$\Sigma$	\Sigma
$\varsigma$	\varsigma
$\tau$	\tau
$\upsilon$	\upsilon
$\phi$	\phi	$\Phi$	\Phi
$\varphi$	\varphi
$\chi$	\chi
$\psi$	\psi	$\Psi$	\Psi
$\omega$	\omega	$\Omega$	\Omega

Common Relation Symbols

All relation symbols can be prefixed with \not to denote negation.

Symbol	Code
$\neq$	\neq or \not=
$\leq$	\leq or \le
$\geq$	\geq or \ge
$\ll$	\ll
$\gg$	\gg
$\subset$	\subset
$\supset$	\supset
$\subseteq$	\subseteq
$\supseteq$	\supseteq
$\in$	\in
$\ni$	\ni
$\bigcup$	\bigcup
$\bigcap$	\bigcap
$\propto$	\propto
$\infty$	\infty

Special Symbols

Symbol	Code
$\leftarrow$	\leftarrow
$\Leftarrow$	\Leftarrow
$\rightarrow$	\rightarrow
$\Rightarrow$	\Rightarrow
$\leftrightarrow$	\leftrightarrow
$\Leftrightarrow$	\Leftrightarrow
$\leftharpoonup$	\leftharpoonup
$\leftharpoondown$	\leftharpoondown
$\rightharpoondown$	\rightharpoonup
$\rightharpoondown$	\rightharpoondown
$\leftrightharpoons$	\leftrightharpoons

Special Fonts

Font Style	Code
$\mathrm{ABCdef}$	\mathrm{ABCdef}
$\mathit{ABCdef}$	\mathit{ABCdef}
$\mathnormal{ABCdef}$	\mathnormal{ABCdef}
$\mathcal{ABC}$	\mathcal{ABC}
$\mathscr{ABC}$	\mathscr{ABC}
$\mathfrak{ABCdef}$	\mathfrak{ABCdef}
$\mathbb{ABC}$	\mathbb{ABC}

5. Text Styling

Text Color

$\color{blue}{文字}$             %文字颜色
$\color[rgb]{0.9,0.1,0.2}{文字}$%rgb三个参数取值[0,1]

$\color{blue}{文字}$ \color[rgb]{0.9,0.1,0.2}{文字}

Text Highlight

$\colorbox{green}{文字}$              %文字颜色
$\colorbox{yellow}{\color{red}{文字}}$%复合用法

$\colorbox{green}{文字}$ $\colorbox{yellow}{\color{red}{文字}}$