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$ \picture(350,250){(25,25){\line(300,0)}(25,25){\line(0,220)}(25,245){\line(300,-220)}(310,25){\circle(100;135,180)}(20,100){\line(310,-75)} (25,25){\fbox{\line(5,5)}}(25,25){\line(150,150)}(165,140){Hypotenuse}(120,2){Adjacent}(2,80){\rotatebox{90}{Opposite}}(270,40){\theta}}$

apostrophe $'$ vs super-prime ${}^{\prime}$

str inside backtick: xyz

$\overset{a}{b} \overset{\tiny\text{def}}{=}$

test $A\rightarrow^gy\Rightarrow^km\longrightarrow^w_bp$


벡터표현 using 특수문자
2v⃗+w⃗=0⃗
a⃗b⃗c⃗d⃗e⃗f⃗g⃗
A⃗B⃗C⃗D⃗E⃗f⃗G⃗
벡터표현 using mathml
v

$\overset\leftrightarrow{abdefghkjlhlkh;lkh}$



show referer:
https://www.whatismyreferer.com/
http://www.whatsmyreferer.com/ 나에게 리퍼러를 보여다오

$\version \oint \oiint \oiiint \iint \iiint $


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Jacobian

$J\left(\frac{x,y}{r,\theta}\right)=\left|\begin{array}{cc}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta}\\\frac{\partial y}{\partial r}&\frac{\partial y}{\partial \theta}\end{array}\right|=\left|\begin{array}{cc}\cos\theta&-r\sin\theta\\\sin\theta&r\cos\theta\end{array}\right|=r\cos^2\theta+r\sin^2\theta=r$

$\int dx\int dyf(x,y)=\int dr\int d\theta \underline{r} f(r\cos\theta,r\sin\theta)$
(r is Jacobian)

if there is another symmetry
$\int drd\theta r f(r,\theta)$
$=\int dr r \int d\theta f(r)$
$=\int dr [r f(r)]\int_0^{2\pi}d\theta$
$=\int dr [2\pi rf(r)]$
$=\int (dr)(2\pi r)[f(r)]$ -- user 2017-12-17 04:27:51