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 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.
The required textbook is
Complex Made Simple by David C. Ullrich,
American Mathematical Society, 2008, ISBN 978-0-8218-4479-3.
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 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
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
- 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 firstname.lastname@example.org. Telephone messages can be left at the main office of the Department of Mathematics, 979-845-7554.