Math 617
Theory of Functions of a Complex Variable I
Fall 2015
 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
Functions of One Complex Variable I, second edition, by John B. Conway, published by SpringerVerlag 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 I–VI.
 Prerequisite

The official prerequisite for this course is
Math 410 (real calculus in Euclidean space). The essential background you need is some facility with proofs in the ε–δ style.
 Meeting time and place
 The course meets 2:20–3:35 on Tuesday and Thursday afternoons in room 223 of the Civil Engineering Building.
 Exams and grades


The two midterm exams are scheduled for October 1 (Thursday) and November 5 (Thursday). Each of these exams counts for 25% of the course grade.

The cumulative final examination,
which takes place 1:00–3:00 on the afternoon of December 16 (Wednesday), 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/6172015c/
 Office hours

During the Fall 2015 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.