This is an archived course. A more recent version may be available at ocw.mit.edu.
Lectures: 2 sessions / week, 1.5 hours / session
Analysis I (18.100B)
Strauss, Walter A. Partial Differential Equations: An Introduction. New York, NY: Wiley, March 3, 1992. ISBN: 9780471548683.
John, Fritz. Partial Differential Equations (Applied Mathematical Sciences). 4th ed. New York, NY: Springer-Verlag, March 1, 1982. ISBN: 9780387906096.
There are eleven problem sets, two midterm exams, and a final exam. There is a problem set handed out every week, and due in class on the session of the following week.
The grade will be based on:
| ACTIVITIES | PERCENTAGES |
|---|---|
| Weekly homework | 25% |
| Two mid-term exams (20% each) | 40% |
| Final exam | 35% |
| LEC # | TOPICS | HANDOUTS |
|---|---|---|
| 1 | Introduction and basic facts about PDE's | |
| 2 |
First-order linear PDE's PDE's from physics | |
| 3 | Initial and boundary values problems | |
| 4 |
Types of PDE's Distributions | |
| 5 | Distributions (cont.) | Problem set 1 due |
| 6 | The wave equation | |
| 7 | The heat/diffusion equation | Problem set 2 due |
| 8 |
The heat/diffusion equation (cont.) Review | Problem set 3 due |
| First mid-term | ||
| 9 | Fourier transform | |
| 10 | Solution of the heat and wave equations in Rn via the Fourier transform | Problem set 4 due |
| 11 | The inversion formula for the Fourier transform, tempered distributions, convolutions, solutions of PDE's by Fourier transform | |
| 12 | Tempered distributions, convolutions, solutions of PDE's by Fourier transform (cont.) | Problem set 5 due |
| 13 | Heat and wave Equations in half space and in intervals | |
| 14 | Inhomogeneous PDE's | Problem set 6 due |
| 15 | Inhomogeneous PDE's (cont.) | |
| 16 | Spectral methods - separation of variables | Problem set 7 due |
| 17 | Spectral methods - separation of variables (cont.) | Problem set 8 due |
| Second mid-term | ||
| 18 | (Generalized) Fourier series | Problem set 9 due |
| 19 | (Generalized) Fourier series (cont.) | |
| 20 | Convergence of Fourier series and L2 theory | |
| 21 | Inhomogeneous problems | Problem set 10 due |
| 22 | Laplace's equation and special domains | |
| 23 | Poisson formula | Problem set 11 due |
| Final exam |
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