Notes will be posted here in the afternoons following the lecture.
Lecture Notes |
Date |
Topic |
|
|---|---|---|---|
| #1 | | Wednesday, | Sept. 4 Preview of the course | |
| #2 | | Friday, | Sept. 6 Geometry of complex numbers | |
| #3 | | Wednesday, | Sept. 11 Cauchy Riemann equations | |
| #4 | | Friday, | Sept. 13 more on C-R eqns, polynomials, rat'l functions | |
| #5 | | Monday, | Sept. 16 power series | |
| #6 | | Wednesday, | Sept. 18 exponential, trig functions | |
| #7 | | Friday, | Sept. 20 logarithm, multi-valued functions | |
| #8 | | Monday, | Sept. 23 topology of metric spaces | |
| #9 | | Wednesday, | Sept. 25 complex line integrals | | #10 | | Friday, | Sept. 27 independence of path, Cauchy's Thm for rectangles | |
#11 | | Monday, | Sept. 30 Cauchy's Thm for disks, isolated singularities | |
#12 | | Wednesday, | Oct. 2 Cauchy integral formual, winding number | |
#13 | | Friday, | Oct. 4 winding numbers, derivatives via integral formula | |
#14 | | Monday, | Oct. 7 integral formula as convolution (notes a bit messy, should be rewritten...) | |
#15 | | Wednesday, | Oct. 9 (finite) Taylor expansions | |
#16 | | Friday, | Oct. 11 isolated zeros of analytic functions | |
#17 | | Monday, | Oct. 21 Open mapping thm, Maximum modulus principle | |
#18 | | Wednesday, | Oct. 23 applications of maximum modulus principle | |
#19 | | Friday, | Oct. 25 maximum modulus principle in unbounded domains | |
#20 | | Monday, | Oct. 28 Dixon's proof of Cauchy's theorems | |
#21 | | Wednesday, | Oct. 30 Topology and Cauchy's theorems | |
#22 | | Friday, | Nov. 1 Meromorphic functions | |
#23 | | Monday, | Nov. 4 The residue theorem | |
#24 | | Wednesday, | Nov. 6 Power series, Laurent series | |
#25 | | Friday, | Nov. 8 The argument principle | |
#26 | | Monday, | Nov. 11 Improper (real) integrals | |
#27 | | Wednesday, | Nov. 13 Improper integrals and singularities, branch points | |
#28 | | Friday, | Nov. 15 Gamma function | |
#29 | | Wednesday, | Nov. 20 Residues at infinity and integrals over branch cuts | |
#30 | | Friday, | Nov. 22 Rudiments of Fourier theory | |
#31 | | Monday, | Nov. 25 Mittag-Leffler theorem | |
#32 | | Wednesday, | Nov. 27 Infinite products | |
#33 | | Monday, | Dec. 2 Weierstrass products | |
#34 | | Wednesday, | Dec. 4 Representations of the Gamma function | |
#35 | | Friday, | Dec. 6 Analytic continuation of the zeta function | |
#36 | | Monday, | Dec. 9 Functional equation of the zeta function | |
#37 | | Wednesday, | Dec. 11 Prime number theorem sketch | |
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