MATH 6321 Complex Analysis
Spring 2009
MW 3-4:30 Skiles 133b
Office Hours: MW 4:30-5:30 in Skiles 224
If you have problem to meet me during the scheduled time, email me to
set an appointment.
Syllabus
See online syllabus at MATH
6321
Prerequisite
MATH 4317, 4320
Textbook
Gerald B. Folland, "Real Analysis", Wiley Inter-Science, 2nd Edition.
Grading
I will collect HW every 2 weeks for a total of 5/6 HW. On top there
will be two in class midterms and a in class final. Midterms and final
will be cumulative. The possibility of personal project will be
discussed later during the class. The grading scheme will be 15% HW,
35% midterms and 50% final.
First week
- Material covered
-
I.1 to I.6: The complex Number
-
II.1 to II.6: Metric Spaces and the Topology of C
- Exercises
- I.6: 4
- II.2: 4
- II.4: 5
- II.5: 4, 9
- II.6: 1
Second week
- Material covered
-
III.1: Power series
-
III.2: Analytic function (first part)
- Exercises
- III.1: 6, 7
- III.2: 2, 6, 15
Fourth week
- Material covered
-
III.2: Analytic function (second part)
- III.3: Analityc Function as mapping. Möbius transformations.
- Exercises
Fifth week- Material covered
-
IV.1: Riemann-Stiltjes integral.
-
IV.2: Power Series reppresentation of analytic functions.
- Exercises
- IV.1: 13, 21,23
- IV.2: 4, 8, 10, 11
Second HW due on February 11. First midterm on Wednesady February 18.
Solution set for first midterm.
Seventh week- Material covered
-
IV.3: Zeros of analytic functions.
-
IV.4: The index of a closed curve.
- IV.5: Cauchy's Theorem and Integral Formula
- Exercises
- IV.3: 8
- IV.4: 3
- IV.5: 1, 7, 10
Eighth week- Material covered
-
IV.6: The homotopic version of Cauchy's Theorem and simple connectivity.
-
IV.7: Counting zeros; the Open Mapping Theorem.
- Exercises
- IV.6: 1, 4, 6, 10
- IV.7: 3, 4
Third HW due on March 23. Here is a pdf file with the exercise from my copy of the textbook.
Second Midterm will be on Wednesday April 1. Solution set for first midterm.