The Fundamental Theorem in Complex Function Theory

Abstract

This introductory chapter is meant to convey the need for and the intrinsic beauty found in passing from a real variable x to a complex variable z. In the first section we “solve” two natural problems using complex analysis. In the second, we state the most important result in the theory of functions of one complex variable that we call the Fundamental Theorem of complex variables; its proof will occupy most of this volume.