Math 618
Theory of Functions of a Complex Variable II
Spring 2016

Course description
This three-credit course is a sequel to Math 617, which is the prerequisite. Topics include infinite products, the Weierstrass factorization theorem, Mittag-Leffler’s theorem, normal families, proof of the Riemann mapping theorem, analytic continuation, Runge’s approximation theorem, conformal mapping, and Picard’s theorems.
Course objectives
By the end of the course, you should be able to
  • explain the theory of convergence and approximation in the space of holomorphic functions;
  • apply the theory of conformal mapping; and
  • analyze the range of holomorphic functions.
Textbook
The required textbook is the same as in Math 617 last semester: Functions of One Complex Variable I, second edition, by John B. Conway, published by Springer-Verlag in 1978. Since the campus library subscribes to a collection of Springer books, registered students can download a pdf copy of the textbook for free. (You may need your TAMU NetID password to download the book.) Paper copies (both hardcover and softcover) are available for purchase from your favorite online bookseller.
The course material is contained in Chapters VII–XII.
Meeting time and place
The course meets 12:45–14:00 on Tuesdays and Thursdays in Thompson 009C Blocker 506A.
Exams and grades
There will be a midterm exam on February 25 (Thursday). The final exam is scheduled for 8:00–10:00 in the morning of Tuesday, May 10. Each exam counts for one third of the course grade. Homework/classwork counts for the remaining third of the course grade.
Course website
http://www.math.tamu.edu/~boas/courses/618-2016a/
Office hours
During the Spring 2016 semester, my office hour in Blocker 601L is on Monday and Wednesday afternoons from 2:00–3:00; I am available also by appointment.
The best way to contact me is via email to boas@tamu.edu. Telephone messages can be left at the Department of Mathematics, 979-845-7554.