Analytic Functions

Abstract

In this chapter, we will define differentiation for single-valued functions of a complex variable, and we will see how the derivative of a complex variable sometimes behaves like the derivative of a real function of one real variable, and other times it is comparable to the partial derivatives of a real function of two real variables. We also learn to appreciate the importance of neighborhoods. If we do not require differentiability in a neighborhood, the smoothness of a function along one path may obscure potential difficulties along some other route.