수식 표현 안내

수학노트
Pythagoras0 (토론 | 기여)님의 2013년 11월 10일 (일) 04:44 판
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웹과 수식표현

HTML 수식표현

웹상에서의 LaTeX을 통한 수식표현


LaTeX 명령어 입문

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LaTeX으로 노트하기


LaTeX 명령예

cases

$$ f(n) = \begin{cases} n/2, & \text{if $n$ is even}\\ 3n+1, & \text{if $n$ is odd} \\ \end{cases} $$

atop

$$\tilde y=\left\{ {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.$$


array

$$ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. $$ $$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$

\[A=\left( \begin{array}{c.cccc}&1&2&\cdots&n\\ 1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)\]


eqnarray

$$\left.\begin{eqnarray} x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}$$


align

\[ \begin{align} & {} \quad \int Y_{l_1}^{m_1}(\theta,\varphi)Y_{l_2}^{m_2}(\theta,\varphi)Y_{l_3}^{m_3}(\theta,\varphi)\,\sin\theta\,\mathrm{d}\theta\,\mathrm{d}\varphi \\ & = \sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi}} \begin{pmatrix} l_1 & l_2 & l_3 \\[8pt] 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} l_1 & l_2 & l_3\\ m_1 & m_2 & m_3 \end{pmatrix} \end{align} \]

\[ \begin{align} \omega_{n} & =\int\cdots\int_{x_1^2+\cdots+x_n^2\leq\ 1} dx_{1}\cdots dx_{n} \\ & = \int_{-1}^{1}\left(\int\cdots \int_{x_1^2+\cdots +x_{n-1}^2\leq\ 1-x_{n}^2} dx_{1}\cdots dx_{n-1}\right)dx_{n} \end{align} \]


underbrace

\[\underbrace{i \hbar \frac{\partial}{\partial t} |\varphi_\pm\rangle = \left( \frac{( \mathbf{p} -e \mathbf A)^2}{2 m} + e \phi \right) \hat 1 \mathbf |\varphi_\pm\rangle }_\mathrm{Schr\ddot{o}dinger~equation} - \underbrace{\frac{e \hbar}{2m}\mathbf{\sigma} \cdot \mathbf B \mathbf |\varphi_\pm\rangle }_\text{Stern Gerlach term}\] 파울리 방정식


substack

$$ \sum_{ \substack{ r,s,t\geq 0 \\ r+s=m,s+t=n}} \frac{q^{rt}}{(q)_r(q)_s(q)_t}=\frac{1}{(q)_{m}(q)_{n}} $$


크기

large

$$ \large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$

Large

$$ \Large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$

LARGE

$$ \LARGE f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$


그리스 문자

$$\alpha \beta \gamma \delta \epsilon (\varepsilon) \zeta \eta \theta (\vartheta) \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi (\varphi) \chi \psi \omega$$

$$A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega$$


글꼴

$$\text{mathcal }\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathscr }\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbb }\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbf }\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbf }\mathbf{abcdefghijklmnopqrstuvwxyz}$$ $$\text{mathfrak }\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathfrak }\mathfrak{abcdefghijklmnopqrstuvwxyz}$$


기타

  • \(\chi(t)=\left(\frac{t}{p}\right)\)
  • \(\operatorname{Re} a > 0 \)
  • \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
  • \(720\div12=60\)
  • $\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$
  • \(\mathcal{H}om\)
  • \(G\"odel\) http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
  • \(\Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}\)
  1. \Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}
  • \(\Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}\)
  1. \Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}


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