MAT 536  Complex Analysis I   Spring 2020 

TuTh 10-11:20am Physics P124

Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: W 1-3pm
MLC hours: F 2:30-3:30pm

Grader: Zhuang Tao, e-mail: zhuang.tao@stonybrook.edu
Grader's office: Math Tower 2-114
Grader's office hours: F 9-10am
Grader's MLC hours: Tue 5-7pm

The Instructor may be reached by e-mail at kamenova@math.stpnybrook.edu.


Description: Elementary functions, holomorphic functions. Cauchy theory, power series, classification of isolated singularities, calculus of residues, open mapping theorem, Riemann mapping theorem.

Syllabus:

1. The field of complex numbers, geometric representation of complex numbers.

2. Analytic functions.

3. Analytic functions as mappings.

4. Complex integration.

5. Local properties of analytic functions.

6. The calculus of residues.

7. Power series.

8. The Riemann mapping theorem.

9. Harmonic functions.


Required book: L. Ahlfors, Complex Analysis, 3rd ed., McGraw-Hill Book Company, 2013.


Grading Policy: Grades will be computed using the following scheme: Homework 30%, Midterm 30%, Final 40%. Students are expected to attend class regularly and to keep up with the material presented in the lectures.


Exams: Midterm - Tuesday, March 24, in class; Final - Friday, May 15, 11:15am-1:45pm in Physics P124.


Homework: (No late homework is accepted)


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