Math 481 Applied PDE --- Spring 2004

Topics by Week

• R. Haberman, Applied Partial Differential Equation, 4th Ed., 2004.

• Week 1: Introduction, derviation of heat equation (1.2), well-posed problem (1.3), equilibrium solutions (1.4), heat equation in higher dimensions (1.5), separation of variables (SOV), boundary value problem, Fourier series (2.1-2.4), other boundary conditions.
• Week 2: Laplace's equation (2.5). More details on Fourier series (3.1-3.3), eigenfunction expansion method (3.4), complex form of Fourier series (3.6).
• Week 3: continue Fourier series (3.3); eigenfunction expansion method (3.4), complex form of Fourier series (3.6); wave equation: formulation, solution by SOV (4.3-4.4); Sturm-Liouville eigenvalue problem (5.1-5.3),
• Week 4: more Sturm-Liouville (5.3-5.4); self-adjoint problems, Legrange and Greens formula (5.5). Boundary conditions of the third kind (5.8).
• Week 5: Higher dimensional problems: rectangular membrane, Helmholtz eqauation (7.2-7.4), Green's formula (7.5), circular domains and Bessel functions (7.7-7.9)
• Week 6: circular domains and Bessel functions (7.7-7.9) Exam 1
• Week 7: Nonhomogeneous problems: heat flow with sources and nonhomogeneous b.c. (8.1), eigenfunction expansion methods (8.3-8.4), Poisson's equation (8.5)
• Week 8: Green's functions for time independent problems: heat equation (9.2), Green's functions for ODEs and delta function (9.3)
• Week 9: Fredholm alternative and generalized Green's functions (9.4); Poisson's equation (9.5)
• Week 10: Problems on infinite domains, Fourier transforms
• Week 11: more Fourier transform examples
• Week 12: Green's functions for time dependent problems; Exam 2.
• Week 13: more of week 11; Laplace transforms:
• Week 14: Catch up!!!
• Week 15:

©2004 Charles Tier