Invitation to Complex Analysis
An ideal choice for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written in an informal style by a master expositor, the book distills more than half a century of experience with the subject into a lucid, engaging, yet rigorous account. The book reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. Written at the level of courses commonly taught in American universities to seniors and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of many intriguing topics that are uncommon in a book at this level. Readers will encounter notions ranging from Landau's notation to overconvergent series to the Phragmén-Lindelöf theorem. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course.The writing is user-friendly in many ways. Each topic is discussed in a typical, commonly encountered situation rather than in the most general, abstract setting. There are no numbered equations. Numerous exercises interspersed in the text encourage readers to test their understanding of new concepts and techniques as they are presented. Detailed solutions of the exercises, included at the back of the book, both serve as models for students and facilitate independent study. Supplementary exercises at the ends of sections, not solved in the book, provide an additional teaching tool.This second edition of Invitation to Complex Analysis has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.
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This book is the edition written by the son of RP Boas. Elder Boas was a very widely know wonderful mathematician from Northwestern Univ, Chicago.
I'm an engineer, but I am heavily into math. The problem with most books written by mathematicians, is that they do not think like engineers.. This book is different. Its much better than the classic Churchhill (what I learned from), or all the other complex analysis books. The first half is the best, with many challenging yet important problems, with solutions in the back, mostly fully worked out. The book approaches complex analysis from the geometric point of view, and instructs how to think gometrically.
I must say I love this book. I really learned a lot from reading it, even after devouring many other classical texts on complex analysis. My goal is to write a yet even better book. I'm not sure I'm up to it, but I'll give it a try. If I succeed, its only because this one is in a class of its own, and I learned from it.
I must thank RP's son for keeping this classic alive.
Jont Allen, Urbana IL (jontallen at i e e e dot org)