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Math Help - Harmonic function

  1. #1
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    Harmonic function

    (a)Show that the function u=x^2+y is not a harmonic function.
    (b)show the function v=x+2y is part of harmonic conjugate and say what f(z) is.


    Any help?!?!:/
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  2. #2
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    Quote Originally Posted by NaNa View Post
    (a)Show that the function u=x^2+y is not a harmonic function.
    \frac{\partial^2u}{\partial x^2}=2
    \frac{\partial^2u}{\partial y^2}=0

    Is \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} equal to 0 ?

    Any thought you've given to your problems ?!?!
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  3. #3
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    is not (du)^2/(dx)^2+(dv)^2/(dy)^2?!?!
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  4. #4
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    in the next one that I have to do is this:
    v=x+2y
    dv/dx=1
    du/dx=dv/dx so u=x+f(y)
    dv/dy=2
    du/dy=dv/dy so u=2y+f(x)

    So v=x+2y
    f(z)=x+2y+i(x+2y)
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