"수식 표현 안내"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
 
(같은 사용자의 중간 판 34개는 보이지 않습니다)
1번째 줄: 1번째 줄:
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==HTML 수식표현[http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols ]==
 
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* [[HTML과 유니코드에서의 수식표현]]
 
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* [[MathJax]]
 
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==웹상에서의 LaTeX을 통한 수식표현==
 
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*  스프링노트<br>
 
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**  편집메뉴에서 '삽입' -> '수식'을 사용<br>
 
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*** 스프링노트 가이드의 [http://help.springnote.com/pages/2901796 수식 삽입하기] 항목 참조
 
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*  구글 문서에서도 수식표현이 가능<br>
 
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** [http://googlesystem.blogspot.com/2009/09/google-docs-has-equation-editor.html Google Docs Has an Equation Editor]<br>
 
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*** Google Operating System, 2009-9-17
 
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*  SITMO<br>
 
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** http://www.sitmo.com/latex/
 
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** 구글이나 스프링노트와는 달리 계정없이 수식이미지를 얻을 수 있음
 
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*  위키피디아<br>
 
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** Wiki의 관련항목에 가서 edit 를 누른뒤, <math></math> 태그 사이에 LaTeX 명령을 써서, preview로 이미지를 얻기
 
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*  MimeTeX<br>
 
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** http://www.forkosh.com/mimetex.html
 
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*  MathJax<br>
 
−
** http://www.mathjax.org/
 
−
** http://geometry.tistory.com/58
 
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==LaTeX 명령어 입문==
 
==LaTeX 명령어 입문==
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*  특정한 수식표현을 배우는 하나의 방법은 Wikipedia를 이용하는 것
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*  특정한 수식표현을 배우는 하나의 방법은 Wikipedia를 이용하는 것<br>
 
 
** Wiki의 관련항목에 가서 edit 를 눌러보면, TeX 명령들을 카피해서 사용가능. 예)[http://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Mascheroni_constant&action=edit&section=5 오일러상수 편집모드]
 
** Wiki의 관련항목에 가서 edit 를 눌러보면, TeX 명령들을 카피해서 사용가능. 예)[http://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Mascheroni_constant&action=edit&section=5 오일러상수 편집모드]
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*  LaTeX 관련 페이지<br>
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*  LaTeX 관련 페이지
 +
** http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols
 
** [http://www.stdout.org/%7Ewinston/latex/ Latex cheat sheet 페이지도 한번 읽어볼 것]
 
** [http://www.stdout.org/%7Ewinston/latex/ Latex cheat sheet 페이지도 한번 읽어볼 것]
 
* http://en.wikibooks.org/wiki/LaTeX
 
* http://en.wikibooks.org/wiki/LaTeX
  
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===모르는 명령어 그림으로 알아내기===
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==모르는 명령어 그림으로 알아내기==
 
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
 
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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==LaTeX으로 노트하기==
 
==LaTeX으로 노트하기==
−
 
 
* [http://math.berkeley.edu/%7Eanton/index.php?m1=me&m2=TeXadvice Advice on realtime TeXing]
 
* [http://math.berkeley.edu/%7Eanton/index.php?m1=me&m2=TeXadvice Advice on realtime TeXing]
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* 한글 TeX http://ajt.ktug.kr/2007/0102khlee.pdf
 
* 한글 TeX http://ajt.ktug.kr/2007/0102khlee.pdf
  
 
   
 
   
 +
==LaTeX 명령예==
 +
===cases===
 +
:<math>
 +
f(n) =
 +
\begin{cases}
 +
n/2, & \text{if </math>n<math> is even}\\
 +
3n+1, & \text{if </math>n<math> is odd} \\
 +
\end{cases}
 +
</math>
  
−
+
:<math>
 +
f(x)=
 +
\begin{cases}
 +
0&x\in[-\pi,\pi]\\
 +
1&x\notin[-\pi,\pi]
 +
\end{cases}
 +
</math>
  
−
   
+
====atop====
 +
:<math>\tilde y=\left\{ {\ddot x\text{ if </math>\vec x<math> odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.</math>
  
−
+
===array===
 +
:<math>
 +
\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.
 +
</math>
 +
:<math>
 +
\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}
 +
</math>
  
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+
:<math>
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+
A=\left(
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==== 하위페이지 ====
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\begin{array}{c.cccc}&1&2&\cdots&n\\
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+
1&a_{11}&a_{12}&\cdots&a_{1n}\\
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* [[수식표현 안내]]<br>
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2&a_{21}&a_{22}&\cdots&a_{2n}\\       
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** [[그리스문자 및 특수문자모음]]<br>
+
\vdots&\vdots&\vdots&\ddots&\vdots\\
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** [[위에 첨자있는 특수문자]]<br>
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n&a_{n1}&a_{n2}&\cdots&a_{nn}
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** [[집합, 관계, 연산기호]]<br>
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\end{array}
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** [[행렬과 연립방정식의 수식표현]]<br>
+
\right)
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** [[화살표 모음]]<br>
+
</math>
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==LaTeX 명령예==
+
===eqnarray===
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'''cases'''
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:<math>\left.\begin{eqnarray}   x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}</math>
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$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \\ \end{cases}$$
 
  
  
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'''연립방정식'''
 
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$$ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. $$
 
  
 +
===align===
 +
:<math>
 +
\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}
 +
</math>
  
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'''array'''
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:<math>
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$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$
+
\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}
 +
</math>
  
−
==예==
+
* http://tex.stackexchange.com/questions/196/eqnarray-vs-align
−
* <math>\mathcal{H}om</math>
 
−
* <math>G\"odel</math>
 
−
* http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
 
  
−
<math>\chi(t)=\left(\frac{t}{p}\right)</math>
 
  
 +
===overbrace/underbrace===
 +
:<math>
 +
\overbrace{ 1+2+\cdots+100 }^{5050}
 +
</math>
  
 +
:<math>\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}</math>
 +
[[파울리 방정식]]
  
−
<math>\operatorname{Re} a > 0 </math>
+
===substack===
 +
:<math>
 +
\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}}
 +
</math>
  
−
 
  
−
* <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
+
===크기===
 +
;large
 +
:<math>
 +
\large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
 +
</math>
 +
;Large
 +
:<math>
 +
\Large f^\prime(x)\ =        \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
 +
</math>
 +
;LARGE
 +
:<math>
 +
\LARGE f^\prime(x)\ =        \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
 +
</math>
  
−
# x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
 
  
−
* <math>e^{i \pi} +1 = 0</math>
+
===그리스 문자===
 +
:<math>\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</math>
  
−
# e^{i\pi}+1=0
+
:<math>A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon
 +
\Phi X \Psi \Omega</math>
  
−
* <math>2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}</math>
 
  
−
# 2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}
+
===글꼴===
 +
:<math>
 +
\begin{array}{l|l}
 +
\text{mathcal }&\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathcal }&\mathcal{abcdefghijklmnopqrstuvwxyz}\\
 +
\text{mathscr }&\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathscr }&\mathscr{abcdefghijklmnopqrstuvwxyz}\\
 +
\text{mathsf }&\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathsf }&\mathsf{abcdefghijklmnopqrstuvwxyz}\\
 +
\text{mathbb }&\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathbb }&\mathbb{abcdefghijklmnopqrstuvwxyz}\\
 +
\text{mathbf }&\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathbf }&\mathbf{abcdefghijklmnopqrstuvwxyz}\\
 +
\text{mathfrak }&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
 +
\text{mathfrak }&\mathfrak{abcdefghijklmnopqrstuvwxyz}
 +
\end{array}
 +
</math>
  
−
* <math>\frac{\sqrt{3}}{5}</math>
+
===기타===
−
 
+
* http://kogler.wordpress.com/2008/03/21/latex-use-of-math-symbols-formulas-and-equations/
−
# \frac{\sqrt{3}}{5}
+
:<math>
 +
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
 +
</math>
  
 +
:<math>
 +
\overset{\alpha}{\omega} \underset{\mu}{\nu} \overset{\beta}{\underset{\Delta}{\tau}} \stackrel{\zeta}{\eta}
 +
</math>
 +
* http://math.stackexchange.com/questions/1032483/how-to-evaluate-int-01-arctan-x2-ln-frac1x22x2-dx/1036425#1036425
 +
:<math>
 +
\begin{align}
 +
\mathscr{I}_2
 +
=&\color{red}{\cancelto{0}{\color{grey}{x\arctan^2{x}\ln{x}\Bigg{|}^1_0}}}-\int^1_0\arctan^2{x}\ {\rm d}x-\int^1_0\frac{2x\arctan{x}\ln{x}}{1+x^2}{\rm d}x\\
 +
=&-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}+2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+3)^2}-\sum^\infty_{n=0}\frac{(-1)^nH_{n}}{(2n+3)^2}\\
 +
=&\frac{\pi^3}{16}-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}-2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+1)^2}+\sum^\infty_{n=1}\frac{(-1)^{n}H_n}{(2n+1)^2}
 +
\end{align}
 +
</math>
 +
* <math>\chi(t)=\left(\frac{t}{p}\right)</math>
 +
* <math>\operatorname{Re} a > 0 </math>
 +
* <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
 
* <math>720\div12=60</math>
 
* <math>720\div12=60</math>
−
 
+
* <math>\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}</math>
−
# 720\div12=60
+
* <math>\mathcal{H}om</math>
−
 
+
* <math>G\"odel</math> http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
−
* <math>\large f^\prime(x)\ =        \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}</math>
 
−
 
 
−
# \large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
 
−
 
 
−
* <math>\Large A\ =\ \large\left(        \begin{array}{c.cccc}&1&2&\cdots&n\\        \hdash 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)</math>
 
−
 
 
−
# \Large A\ =\ \large\left(        \begin{array}{c.cccc}&1&2&\cdots&n\\        \hdash 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)
 
−
 
 
−
* <math>\LARGE\tilde y=\left\{  {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.</math>
 
−
 
 
−
# \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\}
 
−
 
 
−
* <math>\int e^{-\frac{x^2}{2}} dx</math>
 
−
 
 
−
# \int%20e^{-\frac{x^2}{2}}%20dx
 
−
 
 
−
<math>e^x=\lim_{n\to\infty} \left(1+\frac~xn\right)^n</math>
 
−
 
 
−
# e^x=\lim_{n\to\infty} \left(1+\frac~xn\right)^n
 
−
 
 
 
* <math>\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}</math>
 
* <math>\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}</math>
−
 
 
# \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\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}
−
 
 
* <math>\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}}</math>
 
* <math>\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}}</math>
−
 
 
# \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}}
 
# \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}}
  
−
*
+
==메모==
 +
* http://hyperpolyglot.org/math-notation
 +
====HTML 수식표현====
  
−
*  
+
* http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols
 +
* [[HTML과 유니코드에서의 수식표현]]
 +
* [[MathJax]]
  
−
# \sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}
+
====웹상에서의 LaTeX을 통한 수식표현====
−
 
+
*  구글 문서에서도 수식표현이 가능
−
*  
+
** [http://googlesystem.blogspot.com/2009/09/google-docs-has-equation-editor.html 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, <math></math> 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
 +
* 테이블 생성기 http://www.tablesgenerator.com/
  
−
# \int_{a}^{b}f(x)dx=F(b)-F(a)
 
  
−
*  
+
== 관련된 항목들 ==
 +
* [[그리스문자 및 특수문자모음]]
 +
* [[위에 첨자있는 특수문자]]
 +
* [[집합, 관계, 연산기호]]
 +
* [[행렬과 연립방정식의 수식표현]]
 +
* [[화살표 모음]]
  
−
# \exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}
+
[[분류:수식표현]]

2021년 2월 17일 (수) 04:51 기준 최신판

LaTeX 명령어 입문

모르는 명령어 그림으로 알아내기

LaTeX으로 노트하기


LaTeX 명령예

cases

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

\[ f(x)= \begin{cases} 0&x\in[-\pi,\pi]\\ 1&x\notin[-\pi,\pi] \end{cases} \]

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

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

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


overbrace/underbrace

\[ \overbrace{ 1+2+\cdots+100 }^{5050} \]

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

\[ \begin{array}{l|l} \text{mathcal }&\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathcal }&\mathcal{abcdefghijklmnopqrstuvwxyz}\\ \text{mathscr }&\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathscr }&\mathscr{abcdefghijklmnopqrstuvwxyz}\\ \text{mathsf }&\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathsf }&\mathsf{abcdefghijklmnopqrstuvwxyz}\\ \text{mathbb }&\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathbb }&\mathbb{abcdefghijklmnopqrstuvwxyz}\\ \text{mathbf }&\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathbf }&\mathbf{abcdefghijklmnopqrstuvwxyz}\\ \text{mathfrak }&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathfrak }&\mathfrak{abcdefghijklmnopqrstuvwxyz} \end{array} \]

기타

\[ A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C \]

\[ \overset{\alpha}{\omega} \underset{\mu}{\nu} \overset{\beta}{\underset{\Delta}{\tau}} \stackrel{\zeta}{\eta} \]

\[ \begin{align} \mathscr{I}_2 =&\color{red}{\cancelto{0}{\color{grey}{x\arctan^2{x}\ln{x}\Bigg{|}^1_0}}}-\int^1_0\arctan^2{x}\ {\rm d}x-\int^1_0\frac{2x\arctan{x}\ln{x}}{1+x^2}{\rm d}x\\ =&-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}+2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+3)^2}-\sum^\infty_{n=0}\frac{(-1)^nH_{n}}{(2n+3)^2}\\ =&\frac{\pi^3}{16}-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}-2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+1)^2}+\sum^\infty_{n=1}\frac{(-1)^{n}H_n}{(2n+1)^2} \end{align} \]

  • \(\chi(t)=\left(\frac{t}{p}\right)\)
  • \(\operatorname{Re} a > 0 \)
  • \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
  • \(720\div12=60\)
  • \(\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}\)
  • \(\mathcal{H}om\)
  • \(G\"odel\) 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}}

메모

HTML 수식표현

웹상에서의 LaTeX을 통한 수식표현


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