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Lecture Notes

LEC # TOPICS 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 (This resource may not render correctly in a screen reader.PDF)
7 The Heat/Diffusion Equation (This resource may not render correctly in a screen reader.PDF)
8

The Heat/Diffusion Equation (cont.)

Review

 (This resource may not render correctly in a screen reader.PDF)
  First Midterm  
9 Fourier Transform (This resource may not render correctly in a screen reader.PDF)
10 Solution of the Heat and Wave Equations in Rn via the Fourier Transform (This resource may not render correctly in a screen reader.PDF)
11 The Inversion Formula for the Fourier Transform, Tempered Distributions, Convolutions, Solutions of PDE's by Fourier Transform

(This resource may not render correctly in a screen reader.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.) (This resource may not render correctly in a screen reader.PDF)
13 Heat and Wave Equations in Half Space and in Intervals (This resource may not render correctly in a screen reader.PDF)
14 Inhomogeneous PDE's (This resource may not render correctly in a screen reader.PDF - 1.0 MB)
15 Inhomogeneous PDE's (cont.) (This resource may not render correctly in a screen reader.PDF)
16 Spectral Methods - Separation of Variables (This resource may not render correctly in a screen reader.PDF)
17 Spectral Methods - Separation of Variables (cont.) (This resource may not render correctly in a screen reader.PDF)
  Second Midterm  
18 (Generalized) Fourier Series (This resource may not render correctly in a screen reader.PDF)
19 (Generalized) Fourier Series (cont.) (This resource may not render correctly in a screen reader.PDF)
20 Convergence of Fourier Series and L2 Theory (This resource may not render correctly in a screen reader.PDF)
21 Inhomogeneous Problems (This resource may not render correctly in a screen reader.PDF)
22 Laplace's Equation and Special Domains (This resource may not render correctly in a screen reader.PDF)
23 Poisson Formula (This resource may not render correctly in a screen reader.PDF)
  Final Exam