수식 표현 안내

웹과 수식표현

• http://hyperpolyglot.org/math-notation

=HTML 수식표현

• http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols
• HTML과 유니코드에서의 수식표현
• MathJax

웹상에서의 LaTeX을 통한 수식표현

• 구글 문서에서도 수식표현이 가능
  
  • Google Docs Has an Equation Editor
    
    • Google Operating System, 2009-9-17
• SITMO
  
  • http://www.sitmo.com/latex/
  • 구글이나 스프링노트와는 달리 계정없이 수식이미지를 얻을 수 있음
• 위키피디아
  
  • Wiki의 관련항목에 가서 edit 를 누른뒤, \(\) 태그 사이에 LaTeX 명령을 써서, preview로 이미지를 얻기
• MimeTeX
  
  • http://www.forkosh.com/mimetex.html
• MathJax
  
  • http://www.mathjax.org/
  • http://geometry.tistory.com/58

LaTeX 명령어 입문

• 특정한 수식표현을 배우는 하나의 방법은 Wikipedia를 이용하는 것
  
  • Wiki의 관련항목에 가서 edit 를 눌러보면, TeX 명령들을 카피해서 사용가능. 예)오일러상수 편집모드
• LaTeX 관련 페이지
  
  • Latex cheat sheet 페이지도 한번 읽어볼 것
• http://en.wikibooks.org/wiki/LaTeX

모르는 명령어 그림으로 알아내기

• Detexify2 - LaTeX symbol classifier

LaTeX으로 노트하기

• Advice on realtime TeXing

• 한글 TeX http://ajt.ktug.kr/2007/0102khlee.pdf

LaTeX 명령예1

• \(\chi(t)=\left(\frac{t}{p}\right)\)
• \(\operatorname{Re} a > 0 \)
• \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
• \(e^{i \pi} +1 = 0\)
• \(2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}\)
• \(\frac{\sqrt{3}}{5}\)
• \(720\div12=60\)
• \(\large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}\)
• \(\Large A\ =\ \large\left( \begin{array}{c.cccc}&1&2&\cdots&n\\ 1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)\)

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

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

• \(\int e^{-\frac{x^2}{2}} dx\)

$$ \int e^{-\frac{x^2}{2}} dx$$

$$e^x=\lim_{n\to\infty} \left(1+\frac{x}{n}\right)^n$$

$\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}$

$\int_{a}^{b}f(x)dx=F(b)-F(a)$

$\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$

LaTeX 명령예2

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

연립방정식 $$ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. $$

array $$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$

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

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

• http://tex.stackexchange.com/questions/196/eqnarray-vs-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

서체

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

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

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

관련된 항목들

• 그리스문자 및 특수문자모음
• 위에 첨자있는 특수문자
• 집합, 관계, 연산기호
• 행렬과 연립방정식의 수식표현
• 화살표 모음

예

\(\mathcal{H}om\) \(G\"odel\) 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}}