Complex Variables

Math 4036-1
Louisiana State University
Spring Semester, 2021

Prof. Stephen Shipman

Place: Room 243 of Lockett Hall
Time: 1:30-2:50 Tuesday and Thursday

Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@lsu.edu
Office Hours: By Zoom: Monday and Thursday 10:00-11:00 am, or by appointment. The Zoom link is accessible through Moodle.

Course Synopsis

Textbook

Course Description

From the LSU Course Catalog: Analytic functions, integration, power series, residues, and conformal mapping.

Enhanced Description: The concepts of complex variables are genuinely new compared with real-variable analysis. They unify seemingly diverse fields of mathematics as algebra, geometry, analysis, number theory, and topology. In more ways than one, real-variable analysis is a shadow of a more complete, often simpler, geometric or algebraic picture in the complex domain. The crucial point of divergence from real analysis occurs in the derivative of a complex-valued function of a complex variable, which immediately leads to structure that sets it apart from real-variable calculus. In the complex domain, many theories of mathematics and physics and engineering become complete: roots of polynomials, the exponential function and trigonometry, distribution of prime numbers, Fourier analysis, spectral theory, circuit analysis, resonators in physics and engineering, etc. This course introduces the main theorems of complex variables, which lead to fundamental computational techniques, particularly the residue calculus and conformal mapping.