Readings are given for both the required and the optional textbook.
Required Textbook
Strauss, Walter A. Partial Differential Equations: An Introduction. New York: Wiley, 3 March 1992. ISBN: 0471548685.
Optional Textbook
John, Fritz. Partial Differential Equations. 4th ed. Applied Mathematical Sciences. New York: Springer-Verlag, 1 March 1982. ISBN: 0387906096.
Readings Table
| 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, John 3.6 |
| 6 |
The Wave Equation |
Strauss 2.1-2.2, 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 Midterm |
|
| 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, John 5.1 |
| 15 |
Inhomogeneous PDE's (cont.) |
Strauss 3.3-3.4, 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 Midterm |
|
| 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, John 4.5 |
| 21 |
Inhomogeneous Problems |
Strauss 5.6 |
| 22 |
Laplace's Equation and Special Domains |
Strauss 6.1-6.2, John 4.1-4.2 |
| 23 |
Poisson Formula |
Strauss 6.3, John 4.3 |
|
Final Exam |
|
