GES 554: Partial Differential Equations

At the University of Alabama, I taught the GES 554 course Partial Differential Equations from 2014-2017. The course investigated theory, classification, formulation, relevancy, analysis, and solutions of PDEs. Both analytical and computational methods were studied with a special focus on PDEs commonly seen in engineering.

Textbook: Partial Differential Equations for Scientists and Engineers, S. Farlow, Dover ($12 from Amazon) Reviewed here

Notes: The course notes are available for free at: https://charles-oneill.com/ges554/.

2D Wave Equation on a square domain

Topics: The class covered all lessons and problems in Farlow’s book with selected topics and sources supplemented as necessary.

  • Classification and canonical forms
  • Parabolic and diffusion equations, Laplace and Fourier methods
  • Elliptic, BVP equations, Green’s functions
  • Hyperbolic, wave, and non-linear conservation equations
  • Numerical and approximate methods
  • Error analysis and verification & validation
  • Monte Carlo, perturbation and conformal mapping methods
  • Topics at instructor’s discretion
1D Heat Equation with a Fourier Expansion

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