tailieunhanh - A First Course in Complex Analysis

Here is how things change. Originally, the public school curriculum was designed under the assumption that students would, in the main, work on assembly lines, or do physical labor. But assembly lines today are highly mechanized, and much of the current assembly line work demands high level programming and maintenance of robotic mechanisms. Similar changes have occurred with respect to direct physical labor. For example, even 40 years back, dock-work was brutal - lifting and carrying. Today, the vast majority of this work is done by huge robotic mechanisms, and the dock-worker of today spends most of his or her time controlling a very expensive and complex machine or. | A First Course in Complex Analysis Version Matthias Beck Department of Mathematics San Francisco State University San Francisco CA 94132 beck@ Dennis Pixton Department of Mathematical Sciences Binghamton University SUNY Binghamton NY 139o2-6000 dennis@ Gerald Marchesi Department of Mathematical Sciences Binghamton University SUNY Binghamton NY 13902-6000 marchesi@ Lucas Sabalka Department of Mathematics Computer Science Saint Louis University St Louis MO 63112 lsabalka@ Copyright 2002-2012 by the authors. All rights reserved. The most current version of this book is available at the websites http dennis beck . This book may be freely reproduced and distributed provided that it is reproduced in its entirety from the most recent version. This book may not be altered in any way except for changes in format required for printing or other distribution without the permission of the authors. 2 These are the lecture notes of a one-semester undergraduate course which we have taught several times at Binghamton University SUNY and San Francisco State University. For many of our students complex analysis is their first rigorous analysis if not mathematics class they take and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular series and sequences are treated from scratch. This also has the maybe disadvantageous consequence that power series are introduced very late in the course. We thank our students who made many suggestions for and found errors in the text. Special thanks go to Joshua Palmatier Collin Bleak Sharma Pallekonda and Dmytro Savchuk at Binghamton University SUNY for comments after teaching from this book. Contents 1 Complex Numbers 1 Introduction. 1 Definitions and Algebraic Properties. 2 From Algebra to Geometry and Back . 3 Geometric Properties. 6 .