Differential operator
= Differential operator
{wiki}
A differential operator maps a <function> to an expression depending on finitely many of its <derivatives>. A linear differential operator has the form $P=\sum_{|\alpha|\leq m}a_\alpha(x)\partial^\alpha$; its order is the largest derivative order with nonzero coefficient. The <Laplacian> is a second-order example, and <boundary conditions> specify the domain when defining an operator on a <function space>.