# double integral jacobian

• Nov 6th 2010, 07:08 PM
chriswyk628
double integral jacobian
Hi, everyone
I've just joined this forum.
Hope you can help me solve my problem which has bothered me for a long long time.
maybe I've missed sth crucial.

It's about Jacobian of changing variable
http://tutorial.math.lamar.edu/Class...es/eq0029M.gif

http://tutorial.math.lamar.edu/Class...es/eq0033M.gif

1. is it $\displaystyle \displaystyle\frac{\partial(x,y)}{\partial(u,v)}=\ frac{1}{\frac{\partial(u,v)}{\partial(x,y)}}$?

2. if (1) is true, can you show me how to calculate $\displaystyle \frac{\partial(u,v)}{\partial(x,y)}$.
Because I have calculated many times but I find that $\displaystyle \displaystyle\frac{\partial(x,y)}{\partial(u,v)}=\ frac{1}{\frac{\partial(u,v)}{\partial(x,y)}}$ They are not the same

HELP
• Nov 6th 2010, 08:39 PM
tonio
Quote:

Originally Posted by chriswyk628
Hi, everyone
I've just joined this forum.
Hope you can help me solve my problem which has bothered me for a long long time.
maybe I've missed sth crucial.

It's about Jacobian of changing variable
http://tutorial.math.lamar.edu/Class...es/eq0029M.gif

http://tutorial.math.lamar.edu/Class...es/eq0033M.gif

1. is it $\displaystyle \displaystyle\frac{\partial(x,y)}{\partial(u,v)}=\ frac{1}{\frac{\partial(u,v)}{\partial(x,y)}}$?

2. if (1) is true, can you show me how to calculate $\displaystyle \frac{\partial(u,v)}{\partial(x,y)}$.
Because I have calculated many times but I find that $\displaystyle \displaystyle\frac{\partial(x,y)}{\partial(u,v)}=\ frac{1}{\frac{\partial(u,v)}{\partial(x,y)}}$ They are not the same

HELP

Examples? Any particular question?

Tonio