The PDE Song

(to the tune of "Sur le Pont d'Avignon")

Hyperbolic PDE's
have positive discriminants.
For these PDE's we need
pairs of i. c.'s and b. c.'s.
Specify displacement, specify velocity!
And the boundary's Dirichlet:
we have u at boundary D,
For our waves it seems okay:
no chance to go to steady state.

Parabolic PDE's
descriminants are always zero.
We have for these PDE's
a single i. c. and b. c.'s.
Specify initial temperature distribution!
And the boundary's Dirichlet:
we have u at boundary D.
The heat equation's on its way
to steady equilibrium.

Elliptic PDE's
have negative ddiscriminants.
And for these PDE's
all we need is one b. c.
Dirichlet or Neumann, mixed or Robin!
One of these is all we need
for Poisson or for Laplace,
Steady state has been reached;
our problem's time independent.

"The PDE Song" Copyright (c) 2000-2007 Rebecca Hartman-Baker.

Last updated January 22, 2007

hartmanbakrj@ornl.gov