Complex Functions

Abstract

This chapter is an introduction to the theory of analytic functions of single variable. No one can understand the basic concepts of integration without passing through analytic functions. It will be so difficult starting deeply with such functions but the reader should first start from the basic definitions and then slowly develop the ideas of complex analysis to the point that considered the bases to deeper topics such as Cauchy's theorem and the Riemann mapping theorem.

Keywords: Complex-valued function, domain and range of complex-valued function, Cauchy theorem, Riemann mapping theorem, mapping, linear transformation, inverse transformation, bilinear transformation, logarithmic complex function.