Ma 650. Fall 2009.
 
Instructor: Pavel Dubovski
Classes: Mondays 6:15-8:45PM B 124
 
Office hours: MW 2-3 K226 or by appointment.
 

Textbook:

[1] P.DuChateau, D.Zimmermann “Applied Partial Differential Equations”

Syllabus:

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. 1^st order PDEs: characteristics method (sections 7.1, 7.2)

3. Boundary Value problems on spatially bounded domains and Fourier series.

Chapter 3.

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.

Chapter 5.

6. Well posedness.

Chapter 6

7. Generalized solutions and scalar conservation laws.

Sections 7.3, 7.4, 7.5, 7.6

8. Nonlinear 1^st 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.