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Introduction to Partial Differential Equations >> Content Detail



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Readings

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Readings are given for both the required and the optional textbook.



Required Textbook


Amazon logo Strauss, Walter A. Partial Differential Equations: An Introduction. New York, NY: Wiley, March 3, 1992. ISBN: 9780471548683.



Optional Textbook


Amazon logo John, Fritz. Partial Differential Equations (Applied Mathematical Sciences). 4th ed. New York, NY: Springer-Verlag, March 1, 1982. ISBN: 9780387906096.


LEC #TOPICSREADINGS
1Introduction and basic facts about PDE'sStrauss 1.1
2

First-order linear PDE's

PDE's from physics

Strauss 1.2,
John 1.4-1.5

Strauss 1.3-1.4

3Initial and boundary values problemsStrauss 1.4-1.5
4

Types of PDE's

Distributions

Strauss 1.6, John 2.1

Strauss 12.1, John 3.6

5Distributions (cont.)Strauss 12.1, and
John 3.6
6The wave equationStrauss 2.1-2.2, and John 2.4
7The heat/diffusion equationStrauss 2.3-2.4
8

The heat/diffusion equation (cont.)

Review

Strauss 2.3-2.4

Strauss 2.5

First mid-term
9Fourier transformStrauss 12.3, with lecture notes
10Solution of the heat and wave equations in Rn via the Fourier transformStrauss 12.3, with lecture notes
11The inversion formula for the Fourier transform, tempered distributions, convolutions, solutions of PDE's by Fourier transformStrauss 12.3-12.4
12Tempered distributions, convolutions, solutions of PDE's by Fourier transform (cont.)Strauss 12.3-12.4
13Heat and wave equations in half space and in intervalsStrauss 3.2
14Inhomogeneous PDE'sStrauss 3.3-3.4, and John 5.1
15Inhomogeneous PDE's (cont.)Strauss 3.3-3.4, and John 5.1
16Spectral methods - separation of variablesStrauss 4.1-4.3
17Spectral methods - separation of variables (cont.)Strauss 4.1-4.3
Second mid-term
18(Generalized) Fourier seriesStrauss 5.1-5.3
19(Generalized) Fourier series (cont.)Strauss 5.1-5.3
20Convergence of Fourier series and L2 theoryStrauss 5.4-5.5, and John 4.5
21Inhomogeneous problemsStrauss 5.6
22Laplace's equation and special domainsStrauss 6.1-6.2, and John 4.1-4.2
23Poisson formulaStrauss 6.3, and John 4.3
Final exam

 








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