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Functions of One Complex Variable II

  • Textbook
  • © 1995

Overview

Authors:
  1. John B. Conway

    1. Department of Mathematics, University of Tennessee, Knoxville, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 159)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Return to Basics

    • John B. Conway
    Pages 1-27

  3. Conformal Equivalence for Simply Connected Regions

    • John B. Conway
    Pages 29-70

  4. Conformal Equivalence for Finitely Connected Regions

    • John B. Conway
    Pages 71-107

  5. Analytic Covering Maps

    • John B. Conway
    Pages 109-131

  6. De Branges’s Proof of the Bieberbach Conjecture

    • John B. Conway
    Pages 133-167

  7. Some Fundamental Concepts from Analysis

    • John B. Conway
    Pages 169-203

  8. Harmonic Functions Redux

    • John B. Conway
    Pages 205-268

  9. Hardy Spaces on the Disk

    • John B. Conway
    Pages 269-299

  10. Potential Theory in the Plane

    • John B. Conway
    Pages 301-383

  11. Back Matter

    Pages 384-396
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Keywords

About this book

This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat­ ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me. This set a pattern for me in learning new mathematics after I had become a mathematician. Some topics I found satisfactorily treated in some sources; some I read in many books and then recast in my own style. There is also the matter of philosophy and point of view. Going from a certain mathematical vantage point to another is thought by many as being independent of the path; certainly true if your only objective is getting there. But getting there is often half the fun and often there is twice the value in the journey if the path is properly chosen.

Authors and Affiliations

  • Department of Mathematics, University of Tennessee, Knoxville, USA

    John B. Conway

Bibliographic Information

  • Book Title: Functions of One Complex Variable II

  • Authors: John B. Conway

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0817-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1995

  • Hardcover ISBN: 978-0-387-94460-9Published: 19 May 1995

  • Softcover ISBN: 978-1-4612-6911-3Published: 28 September 2012

  • eBook ISBN: 978-1-4612-0817-4Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVI, 396

  • Topics: Potential Theory

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