Mathematics
5022
Spring, 2010
Instructor: Edward N. Wilson
Cupples I, Room 18
E-mail: enwilson@math.wustl.edu
Office Tel: 935-6729 (O.K. to leave messages, better to use e-mail)
Office Hours: MWF 2-3 and by appointment
Class Meeting Times
and Place: MWF 1-2, Cupples I, Room 111
Textbook: Functions of One Complex Variable, by John B. Conway
Springer-Verlag New York Inc., 1973
Homework: As in Math 5021, there will be roughly
one homework assignment per week for a total of approximately 12
assignments. The homework policy for
5022 is the same as for 5021.
Examinations: There will be just one examination, the end of the semester
Complex Variable Qualifying Exam. This will be a three-hour exam covering both the material in Math 5021 (roughly one third of the exam) and the material in Math 5022
(the remaining two thirds). Its style will be similar to the style of the
5021 Final Exam. The instructors of the mathematics Ph.D. qualifying sequences
will try to work out an early May schedule for all five of the qualifying exams
which avoids having two such exams on the same day. This will be announced later.
Grades: Homework will count for 60% of the course grade, the 5022 portion of the qualifying exam for the remaining 40%.
Course Style: The style of the course will be the same as for 5021.
Outline of Topics for the Fall Semester (not
necessarily in the order in which we’ll treat them):
1. Harmonic Functions, Continued. We’ll pick up where we left off in 5021 with the study of harmonic functions, discussing the last few sections in Chapter X of the textbook.
2. The Riemann Mapping Theorem (Chapter VII in the textbook)
3. Analytic Continuation. Our treatment will parallel that in Chapter IX of the textbook but we’ll use different notations.
4. Meromorphic Functions
(i) Infinite series and infinite product expansions;
(ii) Gamma Function, Blaschke products, and Weierstrass doubly periodic functions;
(iii) Jensen’s Theorem and related results.
5. Picard Theorems
6. Additional topics as time permits, e.g., Schwarz-Christoffel transformations
and applications of the Phragmen-Lindelof Theorem.