COMPLEX FUNCTION THEORY

The basics of complex functions will be explained for students of Engineering Sciences, with the aim of being able to use 'complex function theory' as a tool. The goal is not rigor as mathematics, but ease of use that may suit the application. Explanations are based on concrete examples rather than abstract general theory. The book starts from very beginning of complex numbers, and extends theory of Introduction to Elliptic Function and Hypergeometric Differential Equations.

Contents:

• Preface
• Complex Numbers and Functions
• Complex Functions and Holomorphic
• Elementary Functions
• Conformal Transformation
• Singularities
• Complex Integrals
• Cauchy's Integral Formula and Power Series Expansion of Complex Functions
• Advanced Complex Integrals
• Analytic Continuation and Riemann Surface
• Meromorphic Functions
• Elliptic Integrals and Elliptic Functions
• Ordinary Differential Equations of Complex Variables
• Orthogonal Polynomials
• Functions Written With Hypergeometric Functions
• Functions Written With Confluent Hypergeometric Functions
• Bibliography
• Index

Readership: Undergraduate students majoring in engineering and other mathematical sciences.

Key Features:

• The goal of the Book is not rigor as mathematics, but ease of use that may suit the application. Explanations are based on concrete examples rather than abstract general theory