| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Introduction and basic facts about PDE's | Strauss 1.1 |
| 2 | First-order linear PDE's PDE's from physics | Strauss 1.2, Strauss 1.3-1.4 |
| 3 | Initial and boundary values problems | Strauss 1.4-1.5 |
| 4 | Types of PDE's Distributions | Strauss 1.6, John 2.1 Strauss 12.1, John 3.6 |
| 5 | Distributions (cont.) | Strauss 12.1, and John 3.6 |
| 6 | The wave equation | Strauss 2.1-2.2, and John 2.4 |
| 7 | The heat/diffusion equation | Strauss 2.3-2.4 |
| 8 | The heat/diffusion equation (cont.) Review | Strauss 2.3-2.4 Strauss 2.5 |
| First mid-term | ||
| 9 | Fourier transform | Strauss 12.3, with lecture notes |
| 10 | Solution of the heat and wave equations in Rn via the Fourier transform | Strauss 12.3, with lecture notes |
| 11 | The inversion formula for the Fourier transform, tempered distributions, convolutions, solutions of PDE's by Fourier transform | Strauss 12.3-12.4 |
| 12 | Tempered distributions, convolutions, solutions of PDE's by Fourier transform (cont.) | Strauss 12.3-12.4 |
| 13 | Heat and wave equations in half space and in intervals | Strauss 3.2 |
| 14 | Inhomogeneous PDE's | Strauss 3.3-3.4, and John 5.1 |
| 15 | Inhomogeneous PDE's (cont.) | Strauss 3.3-3.4, and John 5.1 |
| 16 | Spectral methods - separation of variables | Strauss 4.1-4.3 |
| 17 | Spectral methods - separation of variables (cont.) | Strauss 4.1-4.3 |
| Second mid-term | ||
| 18 | (Generalized) Fourier series | Strauss 5.1-5.3 |
| 19 | (Generalized) Fourier series (cont.) | Strauss 5.1-5.3 |
| 20 | Convergence of Fourier series and L2 theory | Strauss 5.4-5.5, and John 4.5 |
| 21 | Inhomogeneous problems | Strauss 5.6 |
| 22 | Laplace's equation and special domains | Strauss 6.1-6.2, and John 4.1-4.2 |
| 23 | Poisson formula | Strauss 6.3, and John 4.3 |
| Final exam |
Table of Contents
Study Materials
Readings
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Readings are given for both the required and the optional textbook.
Required Textbook
Strauss, Walter A. Partial Differential Equations: An Introduction. New York, NY: Wiley, March 3, 1992. ISBN: 9780471548683.
Optional Textbook
John, Fritz. Partial Differential Equations (Applied Mathematical Sciences). 4th ed. New York, NY: Springer-Verlag, March 1, 1982. ISBN: 9780387906096.