Math 617
Theory of Functions of a Complex Variable I
Fall 2012

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 complex-analytic functions (holomorphic 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; and the maximum principle and Schwarz's lemma. Additional topics, such as conformal mapping and 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
  • apply complex analysis to compute real integrals.
The required textbook is Invitation to Complex Analysis by Ralph P. Boas, second edition revised by Harold P. Boas, Mathematical Association of America, 2010, ISBN 9780883857649. The course covers the first two chapters (and additional material if time permits).
The official prerequisite for this course is Math 410 (real calculus in Euclidean space).
The course meets 11:10–12:25 on Tuesday and Thursday in room 148 of the Blocker building.
Exams and grades
  • The two midterm exams are scheduled for September 27 (Thursday) and October 25 (Thursday). Each of these exams counts for 25% of the course grade.
  • The cumulative final examination, which has been scheduled by the Registrar for 3:00–5:00 in the afternoon on December 7 (Friday), counts for 25% of the course grade.
  • Homework/classwork counts for the remaining 25% of the course grade.
Course website
Office hours
During the Fall 2012 semester, my office hour in Milner 202 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 Telephone messages can be left at the Milner office of the Department of Mathematics, 979-845-7554.