Graduate Course 3341.504
Complex Analysis
Fall 2017
Instructor: Woo Young Lee
Office: 27-405
Phone: 02-880-1435; E-mail: wylee@snu.ac.kr
Course Meeting Schedule: Mon/Wed 09:30-10:45 (500-L306)
Office Hours: Mon/Wed 13:00-14:00 (27-405)
Teaching Assistant : Jaehui Park (27-430; nephenjia@snu.ac.kr; Office Hour: Mon/Wed 14:00-15:00)
Course Goals: The goal of this course will be for you to develop a systematic knowledge of basic complex Analysis.
This course will cover complex integration, boundary behaviors of Poisson integrals, Schwarz lemma, Runge's theorem,
conformal mappings, infinite products, Jensen's formula, analytic continuation, H^p-spaces, Beurling's theorem,
Banach algebra techniques, and uniform approximation by polynomials.
Prerequisites: A course in measure theory together with basic complex analysis (undergraduate course)
Course Books:
- Required: W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987
- Recommended:
- L.V. Ahlfors, Complex Analysis, 3rd ed., Int. Student Edition, 1979
- W. - J.B. Conway, Functions of one complex variable, 2nd ed., Springer, New York, 1978
- R.G. Douglas, Banach algebra techniques, Springer, New York, 1998
- H. Silverman, Complex Variables, Houghton Mifflin Co. Boston, 1975
Examination and Grading: The course grade will be computed by weighing one midterm exam 40%, the final exam 40%, the assignment 10%.
and attendance will count 10%. The midterm examination will be on Wednesday, November 1st at 6:15 pm
and the final examination will be on wednesday, December 13rd at 6:15 p.m.
Assignment Lists:
|
|
Assignment |
Due day |
|
1 |
Chapter 10, Exercises 1, 2, 3, 4, 7, 10, 11, 13, 20, 22 |
September 18 |
|
2 |
Chapter 11, Exercises 2, 9, 11, 13, 15, 16, 19, 21, 23, 24 |
October 16 |
|
3 |
Chapter 12, Exercises 2, 3, 4, 5, 6, 7, 8, 15 Chapter 13, Exercises 1, 2, 3, 4, 7, 9, 10 |
October 30 |
|
4 |
Chapter 14, Exercises 2, 3, 4, 6, 7, 10, 11, 13 |
November 13 |
|
5 |
Chapter 15, Exercises 1, 2, 4, 9, 14, 18, 22 |
November 20 |
|
6 |
Chapter 16, Exercises 1, 3, 5, 7, 13 |
November 27 |
|
7 |
Chapter 17, Exercises 2, 4, 12, 14, 19, 20, 21 Chapter 18, Exercises 1, 2, 3, 5, 6, 12 |
December 11 |
Solving Problem Seminars: There are 5 solving problem seminars.
T.A. Jaehui Park will help these seminars. Detailed schedule is as follows:
|
|
Date |
Chapter |
Place |
|
1 |
Tuesday, September 19, p.m. 6:15 |
10 |
Announcement in eTL |
|
2 |
Tuesday, October 17, p.m. 6:15 |
11 |
Announcement in eTL |
|
3 |
Tuesday, October 31, p.m. 6:15 |
12-13 |
Announcement in eTL |
|
4 |
Tuesday, November 21, p.m. 6:15 |
14-15 |
Announcement in eTL |
|
6 |
Tuesday, December 12, p.m. 6:15 |
16-18 |
Announcement in eTL |
Detailed Syllabus
|
Week |
Date |
Sections |
Ref |
|
1 |
9/04, 9/06 |
Ch10. Complex differentiation, Integration, Local Cauchy Theorem |
|
|
2 |
9/11, 9/13 |
Ch10. Power series representation, Open mapping theorem, Chains and cycles, Global Cauchy theorem |
|
|
3 |
9/18, 9/20 |
Ch11. Cauchy-Riemann equations, Poisson integral, Mean value property |
|
|
4 |
9/25, 9/27 |
Ch11. Boundary behavior of Poisson integrals |
|
|
5 |
10/02, 10/04 |
Ch11. Representation theorems |
10/04: Holiday |
|
6 |
10/09, 10/11 |
Ch12. Schwarz lemma, Phragmen-Lindelof method |
10/09: Holiday |
|
7 |
10/16, 10/18 |
Ch12. Interpolation theorem Ch13 Approximations by rational functions, Runge's theorem |
|
|
8 |
10/23, 10/25 |
Ch13. Simply connected regions Ch14. Conformal mappings |
|
|
9 |
10/30, 11/01 |
Ch14. Linear fractional transformations, Riemann mapping theorem, Class S |
11/01: Midterm exam |
|
10 |
11/06, 11/08 |
Ch14. Conformal mapping of an annulus Ch15. Infinite products, Jensen's formula |
|
|
11 |
11/13, 11/15 |
Ch15. Zeros of entire functions, Blaschke products Ch16. Regular points and singular points |
|
|
12 |
11/20, 11/22 |
Ch16. Monodromy theorem, Picard theorem Ch17. Subharmonic functions, H^p-spaces |
|
|
13 |
11/27, 11/29 |
Ch17. F. and M. Riesz theorem, Inner-outer factorization |
|
|
14 |
12/04, 12/06 |
Ch17. Beurling's theorem Ch18. Banach algebra techniques |
|
|
15 |
12/11, 12/13 |
Ch20. Uniform approximation by polynomials |
12/13: Final Exam |