# MATH 322 Complex Variables

### Fall 2011

 INSTRUCTOR: John Stockie Office: K 10518 Phone: 778-782-3553 E-mail: stockie  [at]  math.sfu.ca Web: http://www.math.sfu.ca/~stockie/teaching/math322/ CLASS TIMES: MWF  1:30-2:20pm, AQ 3154 MY OFFICE HOUR: Monday  12:30-1:20pm TUTORIAL: The tutorials will be run by Justin Meskas (jmeskas [at] sfu.ca) and are held at the following times:       D101: Thursday  12:30-1:20pm, AQ 5037       D102: Thursday  1:30-2:20pm, AQ 5037 PREREQUISITES: MATH 251. Students with credit for MATH 424 may not take MATH 322 for further credit. TEXTBOOK: Complex Variables with Applications, by JW Brown and RV Churchill (8th edition, McGraw-Hill, 2009). COMMUNICATION: All essential information and course-related materials will be posted on WebCT. I have also set up a Discussion Group, which I encourage you to check and contribute to regularly -- I will try to check it at least a few times a week, but this is mostly for your use. HOMEWORK: Homework will be assigned weekly, usually on Fridays, and will be due the following Friday at 3:30pm. Deposit your homework assignments in the "MATH 322" drop box #10 located in the hallway outside of room K 9509 (do NOT leave your assignment with me). Late assignments are not accepted and will be assigned a mark of zero. COMPUTING: Maple and Matlab will be used occasionally for examples in lectures as well as on homework assignments. Both packages can be accessed from the Assignment Lab in AQ 3144.
 OUTLINE: Complex numbers arise when the familiar arithmetic of the real number system is supplemented by the square root of -1. This course is an introduction to complex analysis, which is a specialized calculus involving functions of a complex variable. At the heart of complex analysis is the class of analytic functions, which are defined in terms of their differentiability properties. The primary goal of this course is to understand the many amazing properties with which these complex-valued functions are endowed. The highlights of the course include: discussions and proofs of the elementary theorems of analytic function theory; series representations of functions; methods for evaluating complex-valued contour integrals; and the geometry of conformal mappings. Some computer-based experimentation and visualization will accompany the lectures and assigned homework. The rudiments of numerical computing and graphics will be introduced through the use and modification of Matlab scripts and Maple workshops posted on the web. The overlap between complex variable theory and other branches of mathematics includes areas such as geometry, topology, number theory, and Fourier analysis. Applications from these and other areas will be discussed during the semester.

MARKING SCHEME:
 Assignments: approx. 30% Midterm Test: approx. 30% Final Exam: approx. 40%