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Lecture notes files.
1 |
Introduction and Basic Facts about PDE's |
(PDF) |
2 |
First-order Linear PDE's
PDE's from Physics
|
(PDF) |
3 |
Initial and Boundary Values Problems |
(PDF) |
4 |
Types of PDE's
Distributions
|
(PDF) |
5 |
Distributions (cont.) |
(PDF) |
6 |
The Wave Equation |
(PDF)# |
7 |
The Heat/Diffusion Equation |
(PDF)# |
8 |
The Heat/Diffusion Equation (cont.)
Review
|
(PDF)# |
|
First Midterm |
|
9 |
Fourier Transform |
(PDF)# |
10 |
Solution of the Heat and Wave Equations in Rn via the Fourier Transform |
(PDF)# |
11 |
The Inversion Formula for the Fourier Transform, Tempered Distributions, Convolutions, Solutions of PDE's by Fourier Transform |
(PDF)#
The Fourier Transform - The Inversion Formula (PDF)
The Fourier Transform - Tempered Distributions (PDF)
|
12 |
Tempered Distributions, Convolutions, Solutions of PDE's by Fourier Transform (cont.) |
(PDF)# |
13 |
Heat and Wave Equations in Half Space and in Intervals |
(PDF)# |
14 |
Inhomogeneous PDE's |
(PDF - 1.0 MB)# |
15 |
Inhomogeneous PDE's (cont.) |
(PDF)# |
16 |
Spectral Methods - Separation of Variables |
(PDF)# |
17 |
Spectral Methods - Separation of Variables (cont.) |
(PDF)# |
|
Second Midterm |
|
18 |
(Generalized) Fourier Series |
(PDF)# |
19 |
(Generalized) Fourier Series (cont.) |
(PDF)# |
20 |
Convergence of Fourier Series and L2 Theory |
(PDF)# |
21 |
Inhomogeneous Problems |
(PDF)# |
22 |
Laplace's Equation and Special Domains |
(PDF)# |
23 |
Poisson Formula |
(PDF)# |
|
Final Exam |
|