Math 617
Theory of Functions of a Complex Variable I
Fall 2015

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 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, 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/617-2015c/
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, 979-845-7554.