COMPLEXANALYSIS - LTH

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COMPLEX ANALYSISFall 2006Christer BennewitzM nne ifr n h gre zoneranalytiska funktionersvaret nu dig finna l tap od dlighetens g ta?F. L fflerCopyrightc 2006 by Christer BennewitzPrefaceThese notes are basically a printed version of my lectures in COMPLEXANALYSIS at the University of Lund. As such they present a limited viewof any of the subject matters brought up, caused by the time constraintsone is faced by in a series of lectures. The core of the subject, presentedin Chapter 3, is very strongly influenced by the treatment in Ahlfors Complex Analysis, one of the genuine masterpieces of the subject. Anyreader who wants to find out more is advised to read this prerequisites are in principle the mathematics coursesgiven in the first two semesters in Lund. Most importantly, this in-cludes a reasonably complete discussion of analysis in one and severalvariables and basic facts about series of functions including absoluteand uniform convergence. A course in topology is also useful, but notessential.

Contents Preface i Chapter1. Complexfunctions 1 1.1. Thecomplexnumbersystem 1 1.2. Polarformofcomplexnumbers 4 1.3. Squareroots 5 1.4. Stereographicprojection 7