Crash Course in Complex Analysis

geared towards computer scientists

Posted: 2017-08-02 , Modified: 2017-08-02

Tags: complex analysis, crash course, numerical analysis, numerical integration, polynomials, Chebyshev polynomials

Here are notes for my talk “Crash course in complex analysis” for the Gems of TCS seminar.

For a crash course, see the first chapter in my notes on analytic number theory, http://tiny.cc/annt. Proof sketches are in the handwritten notes.
For applications, see notes here.

Abstract: Calculus on the complex numbers has an entirely different attitude from calculus on the reals. The additional structure of the complex numbers greatly enriches the theory of differentiable functions. I will cover (the many variants of) Cauchy’s Theorem, power (Laurent) series, and various inequalities (Hadamard three-lines and three-circles). I’ll give some applications including convergence rates for polynomial approximations and numerical integration, and a recent application to population recovery.