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, harmonic functions, 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;
• construct harmonic and holomorphic functions having specified properties; 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, TAMU students can download a pdf copy of the textbook for free (using your TAMU NetID password). At the same link, there is an option to purchase a paper copy for $24.99 (plus tax), much cheaper than the list price. (Look for the box labeled “MyCopy softcover.”) If you prefer a hardback, check with your favorite book vendor.
The course material is contained in Chapters VII–XII.

Meeting time and place

The course meets 12:45–2:00 on Tuesday and Thursday afternoons in room 205B 605AX of the Blocker Building.

Exams and grades

There will be a midterm examination on February 21 (Thursday). The final examination is scheduled for 8:00–10:00 in the morning of Tuesday, May 7. Each exam counts for one third of the course grade. Homework/classwork counts for the remaining third of the course grade.

Course website

https://www.math.tamu.edu/~boas/courses/618-2019a/

Office hours

During the Spring 2019 semester, my office hour in Blocker 601L is 2:00–3:00 in the afternoon on Monday and Wednesday; 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 main office of the Department of Mathematics, 979-845-7554.