Theory of Functions of a Complex Variable I
- 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 firstname.lastname@example.org. Telephone messages can be left at the Milner office of the Department of Mathematics, 979-845-7554.