Will Xu's Blog

How to input math formulas using KaTeX plugin.

Common constructs

superscript

1a^2 + b^2 = c^2

1e^{i\pi} + 1 = 0

subscript

1s = a_1 + a_2 + \cdots + a_n

1A_0 = W_{0,0} + W_{0,1} + W_{0,2} + \cdots + W_{0,n}

square root

1y = \sqrt{x}

1y = \sqrt[n]{x}

fraction

1z = \frac{x}{y}

1z = \frac{x}{1+\frac{y}{8}}

Greek Letters

Example

1\alpha, \Alpha

All Greek letters

$\alpha, \Alpha$	$\rightarrow$	\alpha, \Alpha
$\beta, \Beta$	$\rightarrow$	\beta, \Beta
$\gamma, \Gamma$	$\rightarrow$	\gamma, \Gamma
$\delta, \Delta$	$\rightarrow$	\delta, \Delta
$\epsilon, \Epsilon, \varepsilon$	$\rightarrow$	\epsilon, \Epsilon, \varepsilon
$\zeta, \Zeta$	$\rightarrow$	\zeta, \Zeta
$\eta, \Eta$	$\rightarrow$	\eta, \Eta
$\theta, \Theta, \vartheta$	$\rightarrow$	\theta, \Theta, \vartheta
$\iota, \Iota$	$\rightarrow$	\iota, \Iota
$\kappa, \Kappa$	$\rightarrow$	\kappa, \Kappa
$\lambda, \Lambda$	$\rightarrow$	\lambda, \Lambda
$\mu, \Mu$	$\rightarrow$	\mu, \Mu
$\nu, \Nu$	$\rightarrow$	\nu, \Nu
$\xi, \Xi$	$\rightarrow$	\xi, \Xi
$o, O$	$\rightarrow$	o, O
$\pi, \Pi, \varpi$	$\rightarrow$	\pi, \Pi, \varpi
$\rho, \Rho, \varrho$	$\rightarrow$	\rho, \Rho, \varrho
$\sigma, \Sigma, \varsigma$	$\rightarrow$	\sigma, \Sigma, \varsigma
$\tau, \Tau$	$\rightarrow$	\tau, \Tau
$\upsilon, \Upsilon$	$\rightarrow$	\upsilon, \Upsilon
$\phi, \Phi, \varphi$	$\rightarrow$	\phi, \Phi, \varphi
$\chi, \Chi$	$\rightarrow$	\chi, \Chi
$\psi, \Psi$	$\rightarrow$	\psi, \Psi
$\omega, \Omega$	$\rightarrow$	\omega, \Omega

Parenthesis and Brackets

$(x+y)$	$\rightarrow$	(x+y)
$[x+y]$	$\rightarrow$	[x+y]
$\{x+y\}$	$\rightarrow$	\{x+y\}
$\langle x+y \rangle$	$\rightarrow$	\langle x+y \rangle
$\|x+y\|$	$\rightarrow$	\|x+y\|

To make the parenthesis resize dynamically, put \left and \right before parenthesis.

• with \left and \right:

1F = G \left( \frac{m_1 m_2}{r^2} \right)

• without \left and \right:

1F = G ( \frac{m_1 m_2}{r^2} )

To manually control parenthesis size, use \big, \Big, \bigg, \Bigg.

1\big( \Big( \bigg( \Bigg(,
2\big[ \Big[ \bigg[ \Bigg[

Sum and Product

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

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

Modulo

• Binary modulo \bmod

1c = a \bmod b

• Parenthesis modulo \pmod

1a^p \equiv a \pmod{p}

Decorations

$f'$	$\rightarrow$	f'
$f''$	$\rightarrow$	f''
$\dot{x}$	$\rightarrow$	\dot{x}
$\ddot{x}$	$\rightarrow$	\ddot{x}
$\hat{x}$	$\rightarrow$	\hat{x}
$\tilde{x}$	$\rightarrow$	\tilde{x}
$\bar{x}$	$\rightarrow$	\bar{x}
$\vec{x}$	$\rightarrow$	\vec{x}

1\overline{x + y + z}

1\underline{x + y + z}

1\overbrace{x + y + z}^{|A|}

1\underbrace{x + y + z}_{|A|}

Dots

• low dots

1\{0, 1, 2, \ldots\}

• center dots

11 + 2 + \cdots + n

• cdot vs cdots

1x_1 \cdot x_2 \cdot x_3 \cdots x_n

Sets

$\mathbb{N}$	$\rightarrow$	\mathbb{N}
$\mathbb{Q}$	$\rightarrow$	\mathbb{Q}
$\mathbb{R}$	$\rightarrow$	\mathbb{R}
$\mathbb{Z}$	$\rightarrow$	\mathbb{Z}
$\mathbb{C}$	$\rightarrow$	\mathbb{C}

$\emptyset$	$\rightarrow$	\emptyset
$\cup$	$\rightarrow$	\cup
$\cap$	$\rightarrow$	\cap
$\setminus$	$\rightarrow$	\setminus
$\subset$	$\rightarrow$	\subset
$\subseteq$	$\rightarrow$	\subseteq
$\supset$	$\rightarrow$	\supset
$\supseteq$	$\rightarrow$	\supseteq
$\in$	$\rightarrow$	\in
$\ni$	$\rightarrow$	\ni
$\notin$	$\rightarrow$	\notin
$\forall$	$\rightarrow$	\forall
$\exists$	$\rightarrow$	\exists
$\nexists$	$\rightarrow$	\nexists
$\equiv$	$\rightarrow$	\equiv
$\neg$	$\rightarrow$	\neg
$\lor$	$\rightarrow$	\lor
$\land$	$\rightarrow$	\land

Geometry

$\overline{AB}$	$\rightarrow$	\overline{AB}
$\overrightarrow{AB}$	$\rightarrow$	\overrightarrow{AB}
$\angle A$	$\rightarrow$	\angle A
$\triangle ABC$	$\rightarrow$	\triangle ABC
$\square{ABCD}$	$\rightarrow$	\square{ABCD}
$\cong$	$\rightarrow$	\cong
$\sim$	$\rightarrow$	\sim
$\|$	$\rightarrow$	\|
$\perp$	$\rightarrow$	\perp
$45^{\circ}$	$\rightarrow$	45^{\circ}

$\sin(\theta)$	$\rightarrow$	\sin(\theta)
$\cos(\theta)$	$\rightarrow$	\cos(\theta)
$\tan(\theta)$	$\rightarrow$	\tan(\theta)

Calculus

• Derivative

1v = \frac{ds}{dt}, a = \frac{dv}{dt} = \frac{d^2 s}{dt^2}

• Partial

1\frac{\partial^2u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}

• Integral

1\int udv = uv - \int v du

Matrix

• bmatrix for bracket, and pmatrix for parenthesis.

1M(\theta) =
2\begin{bmatrix}
3  \cos(\theta) & -\sin(\theta) & 0 \\
4  \sin(\theta) &  \cos(\theta) & 0 \\
5             0 &             0 & 1 \\
6\end{bmatrix}

Cases

1f(x) =
2\begin{cases}
3  1, & x < 0 \\
4  x + 1, & x >= 0
5\end{cases}