Re: hyperbolic PDEs

Leslaw Bieniasz wrote:
Is it really so? What I see in textbooks is a definition of
hyperbolic equations in the context of linear second order pdes,
where the distinction is made between elliptic, parabolic and hyperbolic
equations based on the value of the delta = b^2 - 4*a*c
I have not seen any such classificiation for first order pdes.

Actually you can extend the definition of an elliptic operator for all
orders. Look for example at a linear partial differential equation with
constant coefficients, given by
P(D)u=sum_(|a|<=N) C_aD^a u
where C_a are constant coefficients, a is a multiindex, and N the order
of the equation.
If for every nonzero Element z
sum_(|a|=N) C_a z^a is different from zero, then the operator P(D) is
said to be elliptic.

SG Martin
.