MA681 Functions of a Complex Variable


Instructor: Nikolay S. Strigul
E-mails: nstrigul@stevens.edu
Office Hours: by appointment

Lectures: Wednesdays 06:15-08:45 pm, Morton 106.
Homeworks: There will be weekly homework assignments.
Exams: There will be Midterm and Final Exams.

Grading:

Course program Course program (PDF)

General comments:

MA681 is a standard graduate-level course in complex analysis. The major objective of this course is to introduce classical topics such as analytic functions, conformal mappings, complex integrals and complex series. The classical results will be rigorously proved and interpreted geometrically. The course will also have a strong emphasis on problem solutions. Numerous homework assignments of different complexity ranging from standard calculation problems to proposition proofs will be offered. Provided that the mandatory material is covered some additional topics may be considered, for example, applications of complex analysis to the equations of mathematical physics and mathematical biology.

Textbooks

1) Theory of Functions of a Complex Variable by A.I. Markushevich
2) Introductory Complex Analysis by R.A. Silverman, A.I. Markushevich
3) Complex Analysis by K. Kodaira
4) Complex Analysis by L.V. Ahlfors


Course program:

Lecture 1. - Complex numbers.

Lecture 2. - Topology. Continuity.

Lecture 3. - Analytic functions.

Lecture 4. - Conformal mapping.

Lecture 5. - Polynomials and rational functions.

Lecture 6. - Exponentials and logarithms.

Lecture 7. - Complex integrals 1.

Lecture 8. - Complex integrals 2.

Lecture 9. - Complex integrals 3.

Lecture 10. - Power series 1.

Lecture 11. - Power series 2.

Lecture 12. - Singular points.

Lecture 13. - The Residue Theorem.

Lecture 14. - Applications.

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