Table of contents - Complex analysis

This is a table of contents for my notes on complex analysis. Topics are mainly those used in physics.

Complex numbers

• Complex arithmetic
• Sums, products and reciprocals of complex numbers
• Complex plane
• Reflection of complex number through a line
• Binomial theorem for complex numbers
• Complex matrix products
• Hermitian matrix theorems
• Complex numbers in polar form
• Argument of a complex number
• Scalar and vector products of complex numbers
• Complex exponentials and Euler's equation
• Powers of complex numbers and De Moivre's formula
• Sums of multiple angles
• Roots of complex numbers
• Sets in the complex plane - terminology
• Continuum sets
• Constant function on a domain
• Stereographic projection and the Riemann sphere
• Stereographic projection of circles

Analytic functions

• Functions of a complex variable
• Inversion mapping
• Exponential mapping
• Joukowski mapping
• Limits of complex functions
• Differentiable complex functions
• L'hopital's rule
• Cauchy-Riemann equations
• Analytic and entire functions
• Constant complex functions

Complex functions

• Analytic continuation
• Branch points and cuts in the complex plane

Complex integration

• Contour integration
• Contour integration around a branch cut