Ma 650. Fall 2009.
Instructor: Pavel Dubovski
Classes: Mondays 6:15-8:45PM B 124
Office hours: MW 2-3 K226 or by appointment.
 P.DuChateau, D.Zimmermann “Applied Partial Differential Equations”
1. Review of Ordinary Differential Equations:
- separable equations
- linear equations with constant coefficients
- Green function for boundary value problems of 2d order
- eigenvalue problems
2. 1st order PDEs: characteristics method (sections 7.1, 7.2)
3. Boundary Value problems on spatially bounded domains and Fourier series.
4. Mathematical models leading to PDEs: vibrating string, heat conduction, diffusion.
Sections 1.1, 1.2, 1.3, 1.4.
5. BVP on unbounded domains.
6. Well posedness.
7. Generalized solutions and scalar conservation laws.
Sections 7.3, 7.4, 7.5, 7.6
8. Nonlinear 1st order equations. Burgers equation, dispersive waves.
9. Other mathematical models.
Traffic flow, Black-Scholes model in finance, flood waves, Burgetrs equation and shock waves, Korteweg-de Vries equation, Solitons, Nonlinear Schrodinger equation, Solitary waves.