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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.
Course readings.
| 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,
John 1.4-1.5
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 |
|