PDE: Physics, Math and Common Sense. Part I: Conservation Law

Source: CFDIinside blog


The course of Partial differential equations (PDEs) usually is a tough one. There is a number of factors contributing to this toughness:

  • PDE course combines the knowledge from calculus, algebra, ordinary differential equations (ODEs), complex analysis and functional analysis. Simply put, there is a lot that you need to know about!
  • PDE methods often (or should I say, mostly?) come from physics, but this aspect is not always emphasized and, as a result, the intuition is lost.
  • There is lots of abstraction in the PDE course material: characteristics, generalized functions (distributions), eigenfunctions, convolutions and etc. Many of these concepts actually have simple interpretations, but again, this is not emphasized.
  • PDEs themselves are tough. In contrast to ODEs, there are no general methods for all kinds of PDEs. The field is young and a bit messy.

This series of posts aims to demystify PDEs and show some general way of handling PDE problems by combining physical intuition and mathematical methods.…