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Order of a Partial Differential Equation

The order of PDE is, similar to the order of an ODE, defined by the order of the highest derivative that appears in the equation:
$\displaystyle \mbox{div }u=\nabla\cdot u$ $\textstyle \equiv$ $\displaystyle 0\hspace{1cm}\rightarrow \mbox{1st order}$  
$\displaystyle \Delta u$ $\textstyle \equiv$ $\displaystyle 0\hspace{1cm}\rightarrow \mbox{2nd order, }\Delta\mbox{: Laplace-Operator}$  
$\displaystyle u_x+u_{xyy}$ $\textstyle \equiv$ $\displaystyle 0\hspace{1cm}\rightarrow \mbox{3rd order}.$  


Heiko Enderling 2003-11-13