Instructor: Dimiter
Vassilev Office :
SMLC
Bldg, Office 326 Email: vassilev@unm.edu
Phone Number: 505 277 2136
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
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;
Syllabus and Homework
– Spring 2011. You should also work-out all past qualifying exams
|
Week |
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 |
Rational approximation: Runge and Mergelyan’s theorems, analytic capacity. |
HW 13 |
|
15. April 29 |
The Gamma function and elliptic functions. |
HW 14 |
|
16. May 2 |
|
|
|
May 9 -14, Finals week |
|
|
Last Day of
Instructions May 7, Saturday.
Holidays: