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Math Help - transforming from spherical coordinates

  1. #1
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    transforming from spherical coordinates

    This question is born from a question relating to Stokes' theorem, where I'm evaluating the surface integral.
    The area I'm confused with is where I need to transform the follwing into speherical polar coordinates:

    <br />
\int\int_{S} (\nabla \times F)\cdot \bold{\hat{n}}\ dS \ = \frac{1}{2}\int\int_S(-yz-3z)\ dS

    where

    x=2\cos\phi\sin\theta\ y=2\sin\phi\sin\theta\ z=2\cos\theta

    how would I transform the above integral into one wrt d\theta\ d\phi?
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  2. #2
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    I think we must know what surface S is.
    Out of curiosity, your " \frac{1}{2}\int\int_S(-yz-3z)\ dS" shouldn't be dA instead of dS?
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  3. #3
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    Quote Originally Posted by bigdoggy View Post
    This question is born from a question relating to Stokes' theorem, where I'm evaluating the surface integral.
    The area I'm confused with is where I need to transform the follwing into speherical polar coordinates:

    <br />
\int\int_{S} (\nabla \times F)\cdot \bold{\hat{n}}\ dS \ = \frac{1}{2}\int\int_S(-yz-3z)\ dS

    where

    x=2\cos\phi\sin\theta\ y=2\sin\phi\sin\theta\ z=2\cos\theta

    how would I transform the above integral into one wrt d\theta\ d\phi?
    Use Jacobian matrix.
    Last edited by mr fantastic; September 19th 2009 at 01:19 AM. Reason: Restored original reply
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  4. #4
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    I think we must know what surface S is.
    Out of curiosity, your " \frac{1}{2}\int\int_S(-yz-3z)\ dS" shouldn't be dA instead of dS?
    The surface is the hemisphere x^2 + y^2 + z^2 = 4 and the boundary curve is the intersection of the hemisphere with the plane  z=0.

    Use Jacobian matrix.
    I've looked on Wikipedia, Jacobian matrix and determinant - Wikipedia, the free encyclopedia, but how would I go from the Jacobian to dS = 4\sin\theta d\phi d\phi ??

    I'm trying to understand how to convert the integral from the surface integral to one which can be evaluated using spherical polar's.[incidentally I know the answer is dS = 4\sin\theta d\phi d\phi but cant figure out how to get to it!]
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  5. #5
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    On this page,http://en.wikipedia.org/wiki/Spheric...rdinate_system shows integration of sherical coordinates,namely the surface element:

    dS=r^2\sin\theta d\phi d\theta

    I'm hoping someone can explain how to come to this...?
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