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
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.
- 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.
- 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.
- HW 2, due Wed, January 25 in class. pp 29-30: 17, 20, 23, 24, 25, 26.
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.
- 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
- Chapter 2: Cauchy's Theorem
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.