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/.
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