Lecture Notes

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	(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

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