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    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  
    ISBN:   978-981-02-4780-5
    981-02-4780-X
       US$49 / £32

     


     

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    Updated on 13 February 2012