Department of Mathematics

 

Spring 2012: MA 530 Functions Of A Complex Variable I
Instructor: Greg Buzzard

Important note: This class is designed for students who want a rigorous, proof-based approach to complex analysis and who may want to continue in research in complex analysis or who may want to take the qualifying exam in complex analysis through the Department of Mathematics. Students interested in applications or qualifying exams in engineering are strongly encouraged to enroll in MA 525 instead of MA 530.

Exams:
There will be two midterm exams, one near the end of February and one in early April, and one final exam.

Final exam: Tuesday, May 1, 1:00p - 3:00p, REC 226

Sample problems for final.
Actual final exam from 2010.

Exam 2 will be Wednesday, April 4, in class.
Solutions for exam 2
Practice problems for exam 2 (not to be turned in). Also include problem 3, the first part of problem 5, and problem 6 from the practice problems for exam 1.
Actual exam 2 from last year.
Exam 1 will be Friday, Oct 8, in class.
Practice problems for exam 1 (not to be turned in). Omit problems 3, 5, and 6.
Actual exam 1 from last year. Replace number 3 by this: 3. Prove that if f is entire and the real part of f is nonzero on the whole plane, then f is constant.


Assignments and info:
HW 1, due Wed, January 18 in class. pp 24-30: 2, 5, 7, 8, 9, 13 (add the condition that the set is connected), 18
HW 2, due Wed, January 25 in class. pp 29-30: 17, 20, 23, 24, 25, 26.
HW 3, due Wed, February 1, in class. Download here.
HW 4, due Wed, February 15, in class. Download here.
HW 5, due Wed, February 22, in class. Download here.
HW 6, due Wed, February 29, in class. Download here.
HW 7, due Wed, March 7, in class. Download here.
HW 8, due Wed, March 21, in class. Download here.
HW 9, due Wed, March 28, in class. Download here.
HW 10, due Wed, April 18, in class. Download here.

Emergency information: In the event of a major campus emergency, course requirements, deadlines, and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor's control. Information about such changes will be posted on this web page and/or distributed via email.

Office hours:
Tue 3:30-4:30, Wed 10:30-11:30 and by appointment

Text: Complex Analysis (Princeton Lectures in Analysis II), E. Stein and R. Shakarchi

The course topics will include the following.

Chapter 1: Preliminaries
Chapter 2: Cauchy's Theorem
Chapter 3: Meromorphic Functions
Chapter 8: Conformal Mappings
Other topics as time permits

Grading: Course grading will be based on two midterms, a final, and regular homework. The distribution will be roughly 20% per midterm, 30% for the final, and 30% for the homework. The lowest two homework scores will be dropped, but in return, late homework will not be accepted.