A COURSE IN COMPLEX ANALYSIS IN ONE VARIABLE
by Martin A Moskowitz (City University of New York Graduate Center)
Contents (71k)
Preface and Acknowledgments (56k)
Chapter 1: First Concepts
Chapter 1.1: Fundamentals of the complex field (162k)
Chapter 1.2: Holomorphic functions (180k)
Chapter 1.3: Some important examples (200k)
Chapter 1.4: The Cauchy-Riemann equations (184k)
Chapter 1.5: Some elementary differential equations (179k)
Chapter 1.6: Conformality (176k)
Chapter 1.7: Power series (173k)
Complex analysis is a beautiful subject — perhaps the single most beautiful; and striking; in mathematics. It presents completely unforeseen results that are of a dramatic; even magical; nature. This invaluable book will convey to the student its excitement and extraordinary character. The exposition is organized in an especially efficient manner; presenting basic complex analysis in around 130 pages; with about 50 exercises. The material constantly relates to and contrasts with that of its sister subject; real analysis. An unusual feature of this book is a short final chapter containing applications of complex analysis to Lie theory.
Since much of the content originated in a one-semester course given at the CUNY Graduate Center; the text will be very suitable for first year graduate students in mathematics who want to learn the basics of this important subject. For advanced undergraduates; there is enough material for a year-long course or; by concentrating on the first three chapters; for one-semester course.
|
