Principal symbol of a partial differential equation
= Principal symbol of a partial differential equation
{title2=$p(x,\xi)$}
= Principal symbol
{synonym}
For a scalar differential operator of order $k$, the principal symbol replaces each order-$k$ derivative $\partial^\alpha$ by $\xi^\alpha$ and discards lower-order terms. For a <quasilinear partial differential equation>, the coefficients are evaluated at the prescribed lower-order data.