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Math Help - Potential Function

  1. #1
    Junior Member
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    Potential Function

    I need help finishing this question. The original question and my work so far are attached.

    Thanks
    Attached Thumbnails Attached Thumbnails Potential Function-problem-6.jpg   Potential Function-question-6.jpg  
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  2. #2
    MHF Contributor
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    I'm with you thus far. Now deduce what phi(z) is inside psi(y,z), just as you found psi(y,z) inside f(x,y,z).

    \frac{\partial \psi}{\partial z} = \frac{\partial f}{\partial z} - 2xyz = 4z - 2ye^{2z}

    And now,

    \frac{\partial \phi}{\partial z} = \frac{\partial \psi}{\partial z} - (-2ye^{2z}) = 4z

    So

    \phi = 2z^2 + C

    Have to dash, but will add a pic later.

    ... Hi there. Yes, just in case a picture helps. Your work so far in balloon sculpture...











    ... and why not determine psi similarly...










    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; December 16th 2009 at 10:41 AM. Reason: pics
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  3. #3
    Junior Member
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    Thanks for the help. The picture really helps.
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