Complex Analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including hydrodynamics and thermodynamics and also in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.

Chapter 1 : Complex Numbers and their Geometrical Representation

Chapter 2 : Analytic Functions

Chapter 3 : Conformal Mappings

Chapter 4 : More About Conformal Mappings (Mapping by Elementary Functions)

Chapter 5 : Power Series and Elementary Functions

Chapter 6 : Complex Integration

Chapter 7 : Argument Principle and Rouche's Theorem

Chapter 8 : The Calculus of Residues