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This page includes the course calendar.
Prerequisite
Analysis I (18.100B)
Textbooks
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.
Assignments and Exams
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.
Grading Policy
The grade will be based on:
Grading criteria.
| ACTIVITIES |
PERCENTAGES |
| Weekly homework |
25% |
| Two mid-term exams (20% each) |
40% |
| Final exam |
35% |
Calendar
Course calendar.
| 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 |
|