This is a second course in the theory of functions of one complex variable. It covers the construction and approximation of holomorphic, entire, and meromorphic functions, including Mittag-Leffler's theorem, the factorization theorems of Weierstrass and Hadamard, and the theorems of Runge and Mergelyan; the concept of simple connectivity; the theory of analytic continuation and the idea of a Riemann surface; Picard's theorems; and applications to some problems in functional analysis and number theory.
The required textbook is Function Theory of One Complex Variable, second edition, by Robert E. Greene and Steven G. Krantz, American Mathematical Society, 2002, ISBN 0-8218-2905-X. The course covers chapters 8-16.
The prerequisite for this course is Math 617.
The course meets Monday, Wednesday, and Friday, 12:40-1:30 P.M., in BLOC 164.
The home page for the course is /~harold.boas/courses/618-2004a/.
The instructor is Dr. Harold P. Boas. The email address is boas@tamu.edu and the telephone number is (979) 845-7269. The instructor's office hours are held in 202 Milner Hall from 10:30 to 11:30 on Monday, Wednesday, and Friday; also by appointment.
In this course, there will be a variety of learning experiences, including in-class work, homework, projects, and a final examination (scheduled by the registrar for 10:30-12:30 on Monday, May 10). The grading scheme will be as follows: A = did most of the work well; B = did most of the work adequately; C = did minimal work; F = failed to complete a substantial amount of the required work.