Complex-valued functions

Defining complex-valued functions

Multivalued functions

Complex continuous functions

Open regions

Analytic continuation

Analytic functions

Circle of convergence

Complex differentiation

Wirtinger derivatives

Holomorphic functions

Complex smooth functions

All differentiable complex functions are smooth

All smooth complex functions are analytic

Complex integration

Singularities

Contour integration

Line integral

Cauchy's integral theorem

Cauchy's integral formula