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.

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 ...

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