Next: §2 Formulae Up: Introduction Previous: Introduction

§1 Motivation

It is possible to simplify many P.D.E.s by using coordinate systems that are special to the problem:

in unsteady pipe flows, use the lines along which sound waves propagate (characteristic lines) as coordinate lines to simplify the P.D.E.;
in steady supersonic flows, use the Mach lines along which disturbances propagate (characteristic lines) as coordinate lines to simplify the P.D.E.;
in problems with anisotropic properties, rotate your coordinate system along the principal or physical directions;
...

Next: §2 Formulae Up: Introduction Previous: Introduction