Math 5423 (Complex Analysis I)

Fall 2011

Instructor:

John Albert

Office: PHSC 1004, Ext. 5-3782.

Office hours: Mon, Wed and Thurs, 10:30-11:30 AM (or by appointment)

E-mail: jalbert@ou.edu

Final exam and solutions.
Solutions to problems on Assignment 8.

I found a nice, simple, lemma you can use to justify taking the derivative inside a line integral, without having to explicitly worry about uniform convergence or things like that. It's stated and proved on pages 7 and 8 of the above problem solutions from Assignment 8.
The answer I gave in the above solutions to problem 16 of chapter 5 omitted something: I should have mentioned that we can assume the function f is nonconstant (and therefore justify using the local mapping property), since otherwise it's obvious that f is not one-to-one on any neighborhood of P.

Solutions to problems on Exam 2.
Exam 2.
Here's a brief note about what the second exam covers.
Solutions to problems on Assignment 7.
Practice problems for the second exam.
Exam 1.
Review for Exam 1.
Here are some practice problems for the first exam.
Here is the syllabus for this course.

Test Dates

Test 1: Friday, Oct. 14

Test 2: Monday, Nov. 21

Final Exam: Tuesday, Dec. 13, 4:30 to 6:30 pm

Assignments

Assignment

Due Date

Problems

1 Friday, Sept. 2 Chapter 1: #4, 8, 12

2 Friday, Sept. 16 Chapter 1: #46, 47, 52; Chapter 2: #4(b,c)

3 Friday, Sept. 23 Chapter 2: #16, 18(a,b,c)

4 Monday, Oct. 3 Chapter 3: #2, 21

5 Monday, Oct. 17 Chapter 3: #20(a,b), 27, 32

6 Monday, Oct. 31 Chapter 4: #5(a,b,e), 13(a,c)

7 Friday, Nov. 11 Chapter 4: # 9, 23, 34(a,d,i)

8 Monday, Dec. 5 Chapter 4: #47, 49 (amended so the denominator is x^3 + x + 2, not x^3 + x + 1), 55; Chapter 5: #6, 15, 16 (For #6 in Chapter 5, you can assume that by "a suitable solution" is meant "a solution g(z) satisfying e^{g(0)} = f(0)", and by "checking that this solution does the job" is meant "checking that e^g(z) = f(z) for all z in D(0,1)".)

Links

http://www.math.ttu.edu/~pearce/complex/complexviewer.html

Assignment	Due Date	Problems
1	Friday, Sept. 2	Chapter 1: #4, 8, 12
2	Friday, Sept. 16	Chapter 1: #46, 47, 52; Chapter 2: #4(b,c)
3	Friday, Sept. 23	Chapter 2: #16, 18(a,b,c)
4	Monday, Oct. 3	Chapter 3: #2, 21
5	Monday, Oct. 17	Chapter 3: #20(a,b), 27, 32
6	Monday, Oct. 31	Chapter 4: #5(a,b,e), 13(a,c)
7	Friday, Nov. 11	Chapter 4: # 9, 23, 34(a,d,i)
8	Monday, Dec. 5	Chapter 4: #47, 49 (amended so the denominator is x^3 + x + 2, not x^3 + x + 1), 55; Chapter 5: #6, 15, 16 (For #6 in Chapter 5, you can assume that by "a suitable solution" is meant "a solution g(z) satisfying e^{g(0)} = f(0)", and by "checking that this solution does the job" is meant "checking that e^g(z) = f(z) for all z in D(0,1)".)