An Introduction to Complex Function Theory

This book provides a rigorous yet elementary introduction to the theory ofanalytic functions of a single complex variable. While presupposing in itsreadership a... » 

This book provides a rigorous yet elementary introduction to the theory ofanalytic functions of a single complex variable. While presupposing in itsreadership a degree of mathematical maturity it insists on no formalprerequisites beyond a sound knowledge of calculus. Starting from basicdefinitions the text slowly and carefully develops the ideas of complexanalysis to the point where such landmarks of the subject as Cauchys theoremthe Riemann mapping theorem and the theorem of MittagLeffler can be treatedwithout sidestepping any issues of rigor. The emphasis throughout is ageometric one most pronounced in the extensive chapter dealing with conformalmapping which amounts essentially to a quotshort coursequot in thatimportant area of complex function theory. Each chapter concludes with a wideselection of exercises ranging from straightforward computations to problemsof a more conceptual and thoughtprovoking nature. «