  Heuristic arguments and order of magnitude estimates for partial differential
equations highlight essential features of the physics they describe. We present
order of magnitude estimates, and their limitations, for the three classic
second order PDEs of mathematical physics (wave, heat, and Laplace equations),
for first order transport equations, and for two non-linear wave equations. It
is beneficial to expose the beginning student to these considerations before
jumping into more rigorous mathematics. Yet these simple arguments are missing
from physics textbooks.
