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Have you seen this PDE before?

  1. Sep 28, 2012 #1
    In the course of my research I came across this PDE
    [itex]\frac{\partial{a_0}}{\partial{x}}\frac{\partial{a_1}}{\partial{y}}-\frac{\partial{a_0}}{\partial{y}}\frac{\partial{a_1}}{\partial{x}}=0.[/itex]
    with both functions depending on x and y.
    I am quite sure I have seen equations of this form before but I do not remember when and where. Maybe someone of you guys can help me?

    Thanks
     
  2. jcsd
  3. Sep 28, 2012 #2

    pasmith

    User Avatar
    Homework Helper

    The left hand side is the determinant of the jacobian matrix
    [tex]
    \left(
    \begin{array}{cc}
    \frac{\partial a_0}{\partial x} & \frac{\partial a_0}{\partial y} \\
    \frac{\partial a_1}{\partial x} & \frac{\partial a_1}{\partial y}
    \end{array}
    \right).
    [/tex]
     
  4. Sep 28, 2012 #3

    jedishrfu

    Staff: Mentor

    isnt this also the curl of some vector function A(x,y,z) ?

    ∇ × A

    the equation shown would be computing the z-component.
     
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