Math 617
Theory of Functions of a Complex Variable I
Fall 2014

Course description
This three-credit course, intended primarily for graduate students in mathematics, addresses the theory of functions of one complex variable. The basic objects of study are holomorphic functions (complex-analytic functions). The course covers the representation of holomorphic functions by power series and by integrals; complex line integrals, Cauchy's integral formula, and some applications; singularities of holomorphic functions, Laurent series, and computation of definite integrals by residues; the maximum principle and Schwarz's lemma, and conformal mapping. Additional topics, such as harmonic functions, will be discussed if time permits.
The qualifying examination in complex analysis is associated with this course and the sequel (Math 618).
Course objectives
By the end of the course, you should be able to
  • analyze holomorphic functions by using infinite series, integrals, and partial differential equations;
  • state and prove the major theorems that distinguish complex analysis from real analysis; and
  • solve half of the problems on past complex analysis qualifying exams.
Textbook
The required textbook is Complex Made Simple by David C. Ullrich, American Mathematical Society, 2008, ISBN 978-0-8218-4479-3.
Prerequisite
The official prerequisite for this course is Math 410 (real calculus in Euclidean space).
Venue
The course meets 11:10–12:25 on Tuesday and Thursday in room 119D of the Zachry Engineering Center.
Exams and grades
  • The two midterm exams are scheduled for October 2 (Thursday) and November 6 (Thursday). Each of these exams counts for 25% of the course grade.
  • The cumulative final examination, which is scheduled for 3:00–5:00 in the afternoon on December 12 (Friday), counts for 25% of the course grade.
  • Homework/classwork counts for the remaining 25% of the course grade.
Course website
http://www.math.tamu.edu/~boas/courses/617-2014c/
Office hours
During the Fall 2014 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.