| LEC # | TOPICS | Lecture Notes |
|---|---|---|
| 1 | Introduction and Basic Facts about PDE's | (PDF) |
| 2 | First-order Linear PDE's PDE's from Physics | (PDF) |
| 3 | Initial and Boundary Values Problems | (PDF) |
| 4 | Types of PDE's Distributions | (PDF) |
| 5 | Distributions (cont.) | (PDF) |
| 6 | The Wave Equation | (PDF)# |
| 7 | The Heat/Diffusion Equation | (PDF)# |
| 8 | The Heat/Diffusion Equation (cont.) Review | (PDF)# |
| First Midterm | ||
| 9 | Fourier Transform | (PDF)# |
| 10 | Solution of the Heat and Wave Equations in Rn via the Fourier Transform | (PDF)# |
| 11 | The Inversion Formula for the Fourier Transform, Tempered Distributions, Convolutions, Solutions of PDE's by Fourier Transform | (PDF)# The Fourier Transform - The Inversion Formula (PDF) The Fourier Transform - Tempered Distributions (PDF) |
| 12 | Tempered Distributions, Convolutions, Solutions of PDE's by Fourier Transform (cont.) | (PDF)# |
| 13 | Heat and Wave Equations in Half Space and in Intervals | (PDF)# |
| 14 | Inhomogeneous PDE's | (PDF - 1.0 MB)# |
| 15 | Inhomogeneous PDE's (cont.) | (PDF)# |
| 16 | Spectral Methods - Separation of Variables | (PDF)# |
| 17 | Spectral Methods - Separation of Variables (cont.) | (PDF)# |
| Second Midterm | ||
| 18 | (Generalized) Fourier Series | (PDF)# |
| 19 | (Generalized) Fourier Series (cont.) | (PDF)# |
| 20 | Convergence of Fourier Series and L2 Theory | (PDF)# |
| 21 | Inhomogeneous Problems | (PDF)# |
| 22 | Laplace's Equation and Special Domains | (PDF)# |
| 23 | Poisson Formula | (PDF)# |
| Final Exam |