Complex Analysis

Summer, 2007                                                         Syllabus                                        MTH 4426/5526

Instructor: Dr. Sergey Belyi

Time and Room: 10:00-11:50 MTWTh MSCX 116

Office Hours: 8:30-10:00 MTWTh, COMPLX 232, ext. 3467

Text: Complex Analysis for Mathematics, Science and Engineering, by Saff and Snider, 3rd Edition

Catalog Description: We will cover Chapters 1—7. Complex numbers, elementary functions and their mappings, complex limits and power series, analytic functions, integrals, contour integral, and Cauchy integral formula.

Prerequisite:MTH 2227 and 3318 or permission of instructor.

Course Objectives: Upon completion of the course, the student should have an understanding of:

1. Complex numbers and the complex plane
2. Analytic functions and Cauchy-Riemann equations.
3. Complex integration and Cauchy’s Theorem.
4. Cauchy’s integral formula and the residue theorem.
5. Conformal mapping and the linear transformation.

Course Requirements:

1. The student is expected to attend each class session and to participate in class discussion.
2. The student is expected to complete all homework assignments punctually.
3. The student is expected to participate in chalkboard work when called upon.

Tests and Grades: Two tests (midterm and final) will be given. Each exam will constitute approximately 50% of the final grade. Students missing a scheduled test will have a zero (0) score recorded.  A final exam will be administered on July 25, 10:00-12:00.

Homework: Homework will be assigned from each section covered. This homework will not be collected, however, test problems will be very similar to the homework problems.