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Math Help - double integral jacobian

  1. #1
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    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




    1. is it \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  \frac{\partial(u,v)}{\partial(x,y)}.
    Because I have calculated many times but I find that \displaystyle\frac{\partial(x,y)}{\partial(u,v)}=\  frac{1}{\frac{\partial(u,v)}{\partial(x,y)}} They are not the same

    HELP
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  2. #2
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    Quote Originally Posted by chriswyk628 View Post
    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




    1. is it \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  \frac{\partial(u,v)}{\partial(x,y)}.
    Because I have calculated many times but I find that \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
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