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MATH322 D100 Complex Variables
Complex Variables • Syllabus • Math 322
Introduction to Complex Analysis
Complex numbers arise when the familiar arithmetic of the real number system is su plemented with the
square root of minus one, √−1. This course will be an introduction to complex analysis, which is a
specialized calculus involving functions that depend on a complex-valued variable. At the heart of
complex analysis is the class of analytic functions that have a derivative with respect to its complex
variable. The goal of this course is to understand the many amazing properties with which these
complex-valued functions are endowed.
The highlights of the course will be: discussions and proofs of the elementary theorems of analytic
function theory; series representations of functions; methods for evaluating complex contour integrals;
and the geometry of conformal mappings. Some numerical and computer visualization will accompany
the lectures and assigned work. The rudiments of numerical computing and graphics will be introduced
through the use and modification of web-posted Matlab scripts and Maple worksheets.
The overlap of complex variable theory with other branches of mathematics include geometry & topology,
number theory, and Fourier analysis. Various of these applications of complex analysis will be discussed
during the term.