Complex Analysis

2

Analytic Functions

2.1 INTRODUCTION

In this chapter, we will define functions of a complex variable and discuss limit, continuity and differentiability for them. In the process, we are led to the notion of analytic functions which play a very important role in the study of complex analysis. In the last part of the chapter, we will discuss harmonic functions and their relationship with the analytic functions.

2.2 FUNCTIONS OF A COMPLEX VARIABLE

Let S be a set of complex numbers. A function f from S to C is defined as a rule which assigns to each z ∈S a number w ∈ C. The number w is called the value of f at z and we write w = f(z). Here, z is the independent variable, w is the dependent variable and f is the complex function of a complex variable ...