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Readings

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 # TOPICS READINGS
1 Introduction and basic facts about PDE's Strauss 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
3 Initial and boundary values problems Strauss 1.4-1.5
4

Types of PDE's

Distributions

Strauss 1.6, John 2.1

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

The heat/diffusion equation (cont.)

Review

Strauss 2.3-2.4

Strauss 2.5
  First mid-term  
9 Fourier transform Strauss 12.3, with lecture notes
10 Solution of the heat and wave equations in Rn via the Fourier transform Strauss 12.3, with lecture notes
11 The inversion formula for the Fourier transform, tempered distributions, convolutions, solutions of PDE's by Fourier transform Strauss 12.3-12.4
12 Tempered distributions, convolutions, solutions of PDE's by Fourier transform (cont.) Strauss 12.3-12.4
13 Heat and wave equations in half space and in intervals Strauss 3.2
14 Inhomogeneous PDE's Strauss 3.3-3.4, and John 5.1
15 Inhomogeneous PDE's (cont.) Strauss 3.3-3.4, and John 5.1
16 Spectral methods - separation of variables Strauss 4.1-4.3
17 Spectral methods - separation of variables (cont.) Strauss 4.1-4.3
  Second mid-term  
18 (Generalized) Fourier series Strauss 5.1-5.3
19 (Generalized) Fourier series (cont.) Strauss 5.1-5.3
20 Convergence of Fourier series and L2 theory Strauss 5.4-5.5, and John 4.5
21 Inhomogeneous problems Strauss 5.6
22 Laplace's equation and special domains Strauss 6.1-6.2, and John 4.1-4.2
23 Poisson formula Strauss 6.3, and John 4.3
  Final exam