25493 Math 562 001 Func of Cmplx Var II TR 1230-1345 MITCH 212.


Instructor: Dimiter Vassilev     Office :  SMLC Bldg, Office 326  Email: vassilev@unm.edu  Phone Number: 505 277 2136


Office Hours: TTh 10:30 -11:30 or drop-in anytime if you have a quick question



Final exam: Thursday, May 12 10:00 a.m.–12:00 p.m.

Students having conflicts with this examination schedule must notify the appropriate instructor before Friday, April 9, 2010. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before April 9, 2010, the instructor shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses. Changes in this examination schedule are not permitted except by formal approval of the instructor’s College Dean.       


Description: The Mittag-Leffler theorem, series and product expansions, introduction to asymptotics and the properties of the gamma and zeta functions. The Riemann mapping theorem, harmonic functions and Dirichlet's problem. Introduction to elliptic functions. Selected topics.  Prerequisite: MATH 561. This course is a continuation of  Math 561, so it might be useful to check  the  HW for MATH561 Fall 2010. Textbook: Function Theory of One Complex Variable: Third Edition (Graduate Studies in Mathematics) (Hardcover) Robert E. Greene and Steven G. Krantz.


Grades: The final grade will be determined by homework (100 points) and a final exam (200 points).  All grades will be posted on WebCT.


Homework:  You can work together on the homework, but you do need to write up your own solutions in your own words. To help the grader, please write your solutions up neatly and clearly and staple the sheets.   Each problem is worth 1 point. I will determine the number of points you have to do in order to receive the possible maximum of 100 points. You will have a chance to turn in more problems at the end of the semester in order to get closer to the desirable number of solved problems.


Missed Exams:  Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given. 


Disability Statement: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs and they should also contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506.  In addition, they should see CATS- Counseling and Therapy Services; Student Health Center (277-4537). (They can help if you suffer from exam anxiety).    




Syllabus and Homework – Spring 2011. You should also work-out all past qualifying exams



Topics Covered

Due Homework. Turn in as many problems as you can do from any homework any time.
1. Jan. 17   HW 1

2. Jan. 24

The Schwarz reflection principle.

Normal families.

HW 2

3. Jan. 31

UNM closed


4. Feb. 7

The Riemann mapping theorem.

HW 3

5. Feb. 14

Harmonic functions: maximum principle, MVP, the Poisson integral, regularity, Harnack’s principle, the Dirichlet problem and sub-harmonic functions, Perron’s method.

HW 4

6. Feb. 21


HW 5

7. Feb. 28


HW 6

8. Mar. 7


HW 7

Mar. 14

Spring Break


9. Mr. 21

Infinite series and products: The zeta function, the Weirstrass factorization theorem, Weirstrasss and Mittag-Leffler theorems.

HW 8

10. Mar. 28


HW 9

11. April 1


HW 10

12. April 8


HW 11

13. April 15

Jensen’s formula and Blaschke products.

HW 12

14. April 22

 Hp  Spaces.


Rational approximation: Runge and Mergelyan’s theorems, analytic capacity.

HW 13

15. April 29

The Gamma function and elliptic  functions. Picard's theorem.

HW 14

16. May 2



May 9 -14, Finals week




Last Day of Instructions May 7, Saturday.


  • Martin Luther Ling, Jr. Day, Holiday January 17, Monday.
  • Spring Recess March 13-20, Sunday – Sunday.