Math 241: Summer 2006

Lecturer: Colin Diemer

Lecture Summary:
Week 1: Reviewed all of 7.6. 12.1 and 12.2 were covered in full, except for the calculations of Fourier coefficients on 655 and 657 and the few quick words on Periodic Extension, which are both deferred to week 2. Section 12.3 was covered, omitting example 4. The discussion of the Gibbs phenomenon and Half-Range expansions are good to read on your own, but not a major concern of ours.
Week 2: 12.5 - all. Singular boundary conditions were not discussed, but it's a quick read and worthwhile. 12.6.1 omitted. 12.6.2 is useful as a good example of a standard Sturm-Liouville problem (Legendre's equation). Covered the relevent formulas and a few properties of the Fourier Integral and the Fourier Transform (15.3-15.4), ignoring applications of the Fourier Transform to PDE's.
Week 3: Separation of variables (13.1). Seperability of Laplace's equation in 2-D and an explicity boundary value calculation (13.5). Seperability of the spherical Laplacian for angular-invariant solutions; appearance of Cauchy-Euler and Legendre solutions.
Week 4: All of Chapter 17; may ignore streamlines/flows, complex hyperbolic functions. Harmonic functions set aside for now, but may come back. All of Chapter 18 covered except for the Cauchy Integral Formula, which will be for next week.
Week 5: The Cauchy Integral Formula. May omit Liouville's Theorem and the proof of the fundamental theorem of algebra, but you should learn it on your own some day because it's awesome. Series (Power and Laurent), residues, poles, singularities, etc. covered in full (19.1-19.4). The Residue Theorem (19.5).

Homework:
Homework 1: Due Monday
Homework 2: Due Tuesday 5/30
The Midterm
Homework 2 solutions
Homework 3: Due Tuesday 6/13 Small typo: "gives" should be "given" in problem b) in part 3.
Homework 4: Due Friday 6/16
Homework 5: Due Wednesday 6/21
Last year's exam. For your reference.You can safely ignore problems 1e and all of problem 5.

Lecture Comments:

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