Please note that initially, all topics and readings are based an earlier version of this course. They are likely to change (or at least, change weeks) as the course progresses. At any rate, I will update this page very often. Bookmark it, and check it frequently to see what's going on in class.
|
Dates |
Topics |
Reading |
Homework |
Miscellaney |
|---|---|---|---|---|
|
8/26-8/28 |
Complex numbers; real vs. complex linearity |
1.1-1.2 |
Friday's lecture will mostly be about
differentiability for mappings f:R^2 -> R^2. |
|
|
8/31-9/4 |
Holomorphic functions. |
1.3-1.5, 2.2 |
On hwk 2, I meant to include a problem asking you
to show that, on a connected set, the conjugate of a harmonic function
and the anti-derivative of a holomorphic function are unique up to
additive constant when they exist. Since I forgot to actually do
this, feel free to use the fact in solving other problems. |
|
|
9/7-9/11 |
Cauchy's Theorem and integral formula |
2.1-2.5 |
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|
|
9/14-9/18 |
Consequences of Cauchy's Theorem |
3.1, 3.4 |
homework 4 |
|
|
9/21-9/25 |
More consequences |
3.2-3.3, 3.5-3.6 |
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|
|
9/28-10/2 |
Isolated singularities; Laurent series |
4.1-4.4 |
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|
10/5-10/9 |
General form of Cauchy's Theorem; the residue
theorem |
11.2-11.4, 4.5-4.6 |
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|
|
10/12-10/16 |
Residue computations; |
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|
There will be no class on Monday 10/12 (I'll be
away at a conference til late afternoon). |
|
10/26-10/30 |
meromorphic functions
and the Riemann sphere |
4.7, 5.1-5.2 |
We will not meet at the usual time on Wed
10/28. Instead we'll meet 5:30-6:30 PM in Hayes-Healy 229. |
|
|
11/2-11/6 |
maximum principle; linear fractional transformations |
5.3-5.5, 6.1-6.3 |
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|
11/9-11/13 |
Riemann mapping theorem |
6.4-6.6 |
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|
11/16-11/20 |
Riemann mapping theorem |
|
homework 11 |
|
|
11/23/09 |
Harmonic functions |
7.1-7.4 |
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|
11/30-12/4 |
More harmonic functions |
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|
12/7-12/9 |
other stuff |
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Take home final exam due
in my mailbox by noon on Tuesday 12/15. |