Have you seen this PDE before?

  • Thread starter Lurian
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
pasmith
Homework Helper
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637
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

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]
 
  • #3
12,747
6,621
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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