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Math Help - Has anyone seen this differential equation?

  1. #1
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    Has anyone seen this differential equation?

    It looks so familiar but I couldn't recall where I've seen this...

    (d^2z/dx^2)^2+2*(dz/(dydx))*(dz/(dxdy)) +(d^2z/dy^2)

    If someone has, could you please point me to some material that explains how this formula was derived and what practical implication it carries.

    Thank you in advance!
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  2. #2
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    Quote Originally Posted by stclouds View Post
    It looks so familiar but I couldn't recall where I've seen this...

    (d^2z/dx^2)^2+2*(dz/(dydx))*(dz/(dxdy)) +(d^2z/dy^2)

    If someone has, could you please point me to some material that explains how this formula was derived and what practical implication it carries.

    Thank you in advance!
    This is an expression. If it is a formula it must contain an equal sign.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by stclouds View Post
    If someone has, could you please point me to some material that explains how this formula was derived and what practical implication it carries.

    Perhaps you meant the operator:

    \left(\dfrac{{\partial }}{{\partial x}}+\dfrac{{\partial }}{{\partial y}}\right)^2(z)=\dfrac{{\partial^2 z}}{{\partial x^2}}+2\dfrac{{\partial^2 z}}{{\partial x \partial y}}+\dfrac{{\partial^2 z}}{{\partial y^2}}

    related to the Taylor polynomial of z=z(x,y) .
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  4. #4
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    That's not it...

    Sorry it may not be an equation. Perhaps more of an operator...

    I was hoping that it's some well known operator like the laplace. Thing is I know what the laplace signifies, ie something like how a surface is accelerating as it moves further away from origin.

    I want to know what the operator above does. It looks like a combination of the laplace plus twice the diagonal rate of change... or something like that.

    But thanks for helping out guys!
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