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## 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 zS 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 ...

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