Math 4150/6150 - Complex Analysis - Fall 2011

Instructor: 
Office:
E-mail:
Neil Lyall
Boyd GSRC 602A
lyall (followed by @math.uga.edu)
Time/Location:
Office Hours:
(to be confirmed)
 MWF
 MW
 Th
12:20-1:10 (Boyd 304)
1:15-2:15   
TBA


Textbook:  Basic Complex Analysis, by Marsden and Hoffman (Third Edition)




Handout on Infinite Series (as covered in Math 3100)



Course description: In this course we will study complex analysis, which is essentially calculus with complex numbers. At first it may seem that this should be harder than calculus with real numbers, but we will see that in many ways working with complex numbers leads to a "simpler" theory. This is entirely due to the fact that complex differentiable (also called analytic or holomorphic) functions behave in a way that is markedly different to that of real differentiable functions, and are much more "rigid" in a sense we will develop. This leads to many nice properties of analytic functions, which in turn lead to beautiful applications of this subject, even to questions that at first glance have nothing to do with complex numbers!
Topics to be covered: Most of chapters 1-4, namely:
Analytic Functions, Cauchy's Theorem, Series Representation of Analytic Function and Calculus of Residues
.
Course objectives: Understanding complex variable concepts and developing computational facility with their applications.

Homework:
Homework will be assigned weekly, see below.
Exams: There will be three in-class "midterm" exams and (of course) a final exam.  ** dates subject to change**

Exam 1: Wednesday 12th of October

Math 4150 version  Math 6150 version
Exam 2: Friday 18th of November 
Math 4150 version  Math 6150 version
Final Exam:
Friday 9th of December 12:00-3:00


Grading: Homework: 30%
Tests: 40% (20% each)
Final: 30%

For full credit, full work must always be shown. Any absence on a test day will result in a test grade of 0. It will be possible to make up for a missed test only if documented justification for the absence is provided.
Calculators:
You may not use calculators on any test unless specifically stated otherwise.




WP/WF policy: The official attendance policy of the university states: 
Students are expected to attend classes regularly. A student who incurs an excessive number of absences may be withdrawn from a class at the discretion of the professor (http://bulletin.uga.edu/bulletin/ind/attendance.html)

In this class, we interpret "excessive" to mean four or more unexcused absences. A student withdrawing after the first exam will receive a WF unless he/she has a marginally passing (D) average in the class (taking into account all relevant data: homework/quiz grades, exams, attendance).


Academic Honesty: As a University of Georgia student, you have agreed to abide by the University’s academic honesty policy, “A Culture of Honesty,” and the Student Honor Code. All academic work must meet the standards described in “A Culture of Honesty” found at: www.uga.edu/honesty. Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor.




Homework

You should be attempting more problems than those assigned for homework

* indicates Math 6150 questions

Homework 1
Due Wednesday August 24

1.1
1, 6, 7, 14*
1.2
1, 4, 6, 10, 22*
1.3
2, 6, 8 (we will discuss the material for questions 6 & 8 on Monday)

Homework 2
Due Wednesday September 7

1.4
3, 5, 19, 20, 21*
1.5
1, 3, 9, 10
1.6
1, 2, 10*

Homework 3
Due Friday September 16

2.1
1, 3, 4, 5, 6*, 8, 9, 12
2.2
1, 5*, 6*, 9

Homework 4
Due Wednesday September 28
2.4
2, 3*, 4, 5, 6, 7, 13, 14*, 15, 16*, 18, 19

Homework 5
Due Friday
October 7

Chapter 1 Review
Chapter 2 Review
1, 4, 9, 10, 11, 13, 15, 19, 27, 33
1, 5, 6, 11, 13, 19, 21

Homework 6
Due Wednesday October 26
3.2
3.3
1, 3, 5, 7, 9, 25*
1, 2, 3, 4, 19

Homework 7
Due Friday November 11
3.3
4.1
4.2
9, 16*
1, 3, 4*, 5, 7, 9*, 11*, 13
1, 3, 4, 6, 10

Homework 8
Due Monday
December 5
3.R
4.3
4.R
1, 3, 14, 15, 18, 25
1, 2*, 3 [undergraduates need only do with a=5 & b=4], 7, 13, 20
1, 2, 3, 5, 7, 13, 23, 24






The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary