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.
Contents:
- First Concepts
- Integration Along a Contour
- The Main Consequences
of Cauchy's Theorem
- Singularities
- Conformal Mappings
- Applications of Complex Analysis to Lie Theory
Readership: Advanced undergraduates and graduate students in mathematics and
physics.
| 160pp |
Pub. date: Apr 2002 |
