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Thread: Harmonic Functions (Complex Analysis)

  1. October 29th 2008, 07:17 PM #1
    shadow_2145
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    Harmonic Functions (Complex Analysis)

    Decide whether each of the following functions u is harmonic, if so, find a harmonic conjugate.

    (1) u(x,y) = x^4 -6x^2y^2 + y^4

    (2) u(x,y) = \frac{x^2}{x^2 + y^2 + 1}

    Can someone walk me through one of these too, please? Thanks!
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  2. October 30th 2008, 02:53 AM #2
    whipflip15
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    OK It is harmonic if it satisfies u_{xx}+x_{yy}=0. Then find the corresponding v which satisfies the C-R equations.

    Do you not have a textbook?
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