Math 6360, Functions of a Complex Variable 2
Semester 2, 2008-09
Course Lecturer:
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer
Course Information:
The material to be covered includes most of Chapter 5 Section 6,
Chapters 6, 7, and part of Chapter 8 of the Ahlfors textbook, is meant to familiarize students with
harmonic functions, including Poisson's Formula and the
Schwarz Reflection Principal, Series and product developments for analytic functions, including
Taylor series, Laurent series, infinite products and the Blaschke product formulas,
canonical product formulas, the Gamma function and Stirling's formula for the Gamma function;
entire functions - Jensen's formula and Hadamard's Theorem, the Riemann zeta function,
its product development and the extension of the zeta function to the whole plane, the
functional equation and the zeros of the zeta-function; normal families of analytic functions;
conformal mapping and Dirichlet's problem, including the Riemann Mapping Theorem,
harmonic functions and Harnack's Principle, subharmonic functions and
Dirichlet's problem; elliptic functions, including simply periodic functions, doubly-periodic
functions, The Weierstrass Pe-function, the modular function; analytic continuation and the
Riemann surface of a function, the monodromy theorem, branch points; Picard's theorem.
Prerequisites:
Math 6350; in addition, instructor consent required for undergraduates.
Course Text:
We will use the text "Complex Analysis" by Lars Ahlfors, McGraw-Hill, 1979.
I also like the book "Functions of One Complex Variable" by John B. Conway, 2nd Edition,
Springer-Verlag, 1978.
Assessment:
- Homework will be assigned every other week or so. The assessment of
homework performance will count for 55% of the final grade.
- Each student will give an oral presentation and write a short paper (around 10 pp.)
on some more advanced area of complex analysis. The presentation will be 25-30 minutes in
length, and will be given the last day of classes. This will be worth 45% of your final grade.
Half of the grade on this project will come from the written exposition, and half from the oral
presentation of it. You are required to listen to your classmates' presentations as well.
- Final exam period: Our final examination period is scheduled for Tuesday, May 5, 2009,
1:30 p.m. -– 4:00 p.m. Keep this time free to give or listen to oral presentations. The written portion
of your project is due at this time.
If you do not hand in your homework or project on time, without a valid excuse, points will be lost from your
grade for that homework or project. Examples of valid excuses are: documented illness
(doctor's letter required), religious observance, and serious family emergency.
Lecture Hours and Venue:
MWF 2 - 2:50 p.m. in ECCR 1B21.
Office Hours:
MWF 3 - 4 p.m., and by appointment.
Homework:
Some Important Names associated with Complex Analysis :
Back to the home page of Judith A. Packer
Last modified January 5, 2009.