Math 530: Complex Analysis

Course Information

Professor: Kiril Datchev
Lectures: Mondays, Wednesdays, and Fridays, 8:30 to 9:20, in UNIV 203.
Office hours: After class, or by appointment, in MATH 602.

Textbook: Introduction to Complex Analysis, by Michael E. Taylor.

We will cover the following topics: Complex numbers and complex-valued functions of one complex variable; differentiation and contour integration; Cauchy’s theorem; Taylor and Laurent series; residues; conformal mapping; special topics.

Grading is based on
  • Almost weekly homework assignments, worth 1/3 of the total grade,
  • two in-class midterm exams, one on Monday 2/13 and one on Monday 4/3, worth 1/3 of the total grade,
  • a final exam, as scheduled here, worth 1/3 of the total grade.

  • Homework

    Homework is due on paper at the beginning of class on Wednesdays. Here are the assignments:

    Homework 1, due January 18th.
    Homework 2, due January 25th.
    Homework 3, due February 1st.
    The first midterm will be in class on Monday, February 13th. Here are some review problems.
    Homework 4, due February 22nd.
    Homework 5, due March 1st.
    Homework 6, due March 8th.
    Homework 7, due March 22nd.
    The second midterm will be in class on Monday, April 3rd. Here are some review problems.
    Homework 8, due April 12th.
    Homework 9, due Friday April 21st.
    The final will be in HAAS G066 from 3:30 to 5:30 on Thursday, May 4th. Here are some review problems.

    Additional Resources

    Below are some books recommended for further reading, which we will also draw from to some extent.

    Complex Analysis by Lars Ahlfors is the classic book in the subject for good reason. It is more methodical and demanding than our book.

    Complex Variables, by Stephen D. Fisher is an easier book than ours, but does not go as far.

    Finally, a list of general policies and procedures can be found here.