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Calendar table
| 1 |
Introduction and Basic Facts about PDE's |
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| 2 |
First-order Linear PDE's
PDE's from Physics |
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| 3 |
Initial and Boundary Values Problems |
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| 4 |
Types of PDE's
Distributions |
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| 5 |
Distributions (cont.) |
Problem set 1 due |
| 6 |
The Wave Equation |
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| 7 |
The Heat/Diffusion Equation |
Problem set 2 due |
| 8 |
The Heat/Diffusion Equation (cont.)
Review |
Problem set 3 due |
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First Midterm |
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| 9 |
Fourier Transform |
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| 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
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| 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 |
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| 14 |
Inhomogeneous PDE's |
Problem set 6 due |
| 15 |
Inhomogeneous PDE's (cont.) |
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| 16 |
Spectral Methods - Separation of Variables |
Problem set 7 due |
| 17 |
Spectral Methods - Separation of Variables (cont.) |
Problem set 8 due |
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Second Midterm |
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| 18 |
(Generalized) Fourier Series |
Problem set 9 due |
| 19 |
(Generalized) Fourier Series (cont.) |
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| 20 |
Convergence of Fourier Series and L2 Theory |
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| 21 |
Inhomogeneous Problems |
Problem set 10 due |
| 22 |
Laplace's Equation and Special Domains |
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| 23 |
Poisson Formula |
Problem set 11 due |
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Final Exam |
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