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Lecture Notes
| 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) |
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First Midterm |
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| 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) |
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Second Midterm |
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| 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) |
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Final Exam |
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