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Laplacian problems

  1. Feb 3, 2004 #1
    Here's the problem:

    Find the Laplacian of sqrt(x^-y^2) and ln(r^2).

    Will i just take the gradient of each one of these twice?
  2. jcsd
  3. Feb 3, 2004 #2

    Tom Mattson

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    No, the Laplacian is (in Cartesian coordinates):

  4. Feb 3, 2004 #3
    is this right?

    For sqrt(x^2-y^2), I got:

    ((x^2-y^2)^-1/2 + x^2(x^2-y^2)^-3/2)i + ((x^2-y^2)^-1/2 -y^2(x^2-y^2)^3/2)j

    I'm not sure how to do the ln(r^2). Can someone help?
  5. Feb 3, 2004 #4


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    ln(r^2)= ln(x^2+ y^2). Does that help?
  6. Feb 3, 2004 #5
    is this right

    First off, did I do the Sqrt(x^2-y^2) right? For ln(r^2), i'm not sure if I'm doing the derivative right. i got, -2/r^3 i
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