Classical Partial Differential Equations (PDE) Cheatsheet

The study of classical PDEs is a useful and typical course for engineers and scientists to both appreciate and understand the behavior of physical systems.

As the (former) instructor of a course in PDEs, I reviewed classical solution techniques in a lecture titled A brief history of GES 554 PDE to prepare students for their final exam. This lecture makes an excellent refresher or rapid introduction.

If you want to review the entire 50 lecture course, visit here. Feel free to call it The Brief History of the World of PDEs in 50 Parts.

Topics covered are:

  • Motivation, classification & canonical forms
  • Diffusion, Elliptic, Hyperbolic, and Transport PDEs
  • Solution methods: Series, Separation of variables, Monte Carlo, finite difference, Ritz / Galerkin and Transforms
  • 1 page PDE toolbox
  • Laplace vs Fourier transforms for PDEs
  • Sturm Liouville Theory
  • Wave Equations
  • Strings, Beams, and Drums
  • Characteristics in transport equations
  • Systems of PDEs: eigenvalues & eigenvectors
  • Green’s Functions
  • Calculus of Variations for PDEs