Math 5522H, Honors Complex
Analysis, Spring 2017
Homework
problems
HOMEWORK 1 Book problems: 4.8, 4.20, 4.21, 4.22, 4.25 (i), (ii),
(iii), 4.33 (i), (ii), (iii), 4.39*,
4.41*, 4.53*,
4.57.
HOMEWORK
2
(4)*
HOMEWORK 3: Book problems: 6.10*,
6.12,
6.21*, 6.25, 6.28, 6.31, 6.36,
6.37, 6.46, 6.48*, 6.51, 6.58
Bonus:
HOMEWORK 3 Book problems: 4.15, 8.1/p. 204 (you can modify the
proof in the book, or the one in class), 8.10, 8.9, 8.12*, 8.16*, 8.18*.
HOMEWORK 4 Book problems: 8.14/P205 8.29*,
8.33, 8.38, 8.43, 8.45*, 8.50* 8.52. .
HOMEWORK 5 Book problems: p 287 and on: 5.8*,
5.11,5.12,5.31,5.33,5.60*,5.88*;
Bonus (20p) Show without using Taylor series (that is only based on
the material leading to Chapter VII) that a function which is
analytic in the unit disk and zero on (-1,1) is identically zero in
the disk.
HOMEWORK 6 Book problems: p 362 and on: 5.8*
(together with V8.38 & I.4.21 if you use them), 5.9, 5.11, 5.12,
5.14* (Note that the range and domain of f
coincide).
HOMEWORK 7 Book problems: p 366 and on: 5.41,5.48, 5.49 (iv), 5.51*, 5.53*, 5.55.
Bonus
Different proof of the residue theorem
HOMEWORK 8 Book problems: p 370 and on: 5.65,5.67,5.69*,5.70*, 5.74, 5.76.
HOMEWORK 9 Book problems: p 468 and on: 6.33 i),ii),iii),6.41,6.42,6.59*,6.60* Bonus