Homepage for Math 207
Complex  Variables
Winter 2009

Enrollment:
gilovich@math.ucsc.edu) at the Math office (195 Baskin Engineering Bld).

Syllabus: pdf

Instructor:
Maria Schonbek
email: schonbek at math dot ucsc dot edu
phone: 459-4657
Office Hours: T: 12am -1,Th2-3, Th 4-5pm.

Lectures: T-Th 2:00-3:45,  Baskin Engineering 379

Textbook:  Complex Variables. Stein and Shakarchi.

Homework:

Homework problems will be assigned on this webpage each  Friday  and will be due the following Thursday.

Homework problems:

HW1: Page 25:
3, 9, 12, 16(c), 20, 25(c)

HW2:
Page 64: 1, 4
Page 64: 2, 7, 8, 10.
Suppose f(z) is entire and Im(f(z)) is bounded, what can you say about the function f(z).

HW3: HW3

HW4: HW4

Hw5

Page 248
:1,3,4,5,8,9,10,12,14,16.

HW6
1. Define a_{2k-1}= -1/sqrt{k} , a_{2k} = 1/sqrt{k}+1/k. Show that
\Pi_{k=1}^{\infty}(1+a_k} cpnverges , but \sum_{k=1}^{\infty} diverges.
From the expansions
\pi cot \pi z -1/z = \sum+{k=1}^{\infty} \frac{2z}{z62-n^2}
deduce
a ) \sum_{k=-\indty}^{\infty}\frac{1}1+n^2}= \pi coth \pi
b) \sum_{n=1}^{\infty} \frac{1}{n^2}= \frac{\p^6}{6}.
Page 155: 6, 9, 11,14

HW7 HW7

FINAL 207