Math 617
Theory of Functions of a Complex Variable I
Fall 2014
 Course description
 This threecredit 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 (complexanalytic 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 9780821844793.
 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/6172014c/
 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, 9798457554.