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  • © 2021

Classical Analysis in the Complex Plane

Birkhäuser

Authors:

  • Covers the classical theory of functions of a single complex variable with depth, precision, and rigor
  • Presents the subject from an authoritative historical perspective, containing more than 2,000 references
  • Offers an exemplary resource for those doing scholarly work on the subject

Part of the book series: Cornerstones (COR)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxix
  2. Prerequisites and Preliminaries

    • Robert B. Burckel
    Pages 1-21
  3. Curves, Connectedness and Convexity

    • Robert B. Burckel
    Pages 23-51
  4. (Complex) Derivative and (Curvilinear) Integrals

    • Robert B. Burckel
    Pages 53-95
  5. Power Series and the Exponential Function

    • Robert B. Burckel
    Pages 97-185
  6. The Index and Some Plane Topology

    • Robert B. Burckel
    Pages 187-260
  7. Schwarz’ Lemma and its Many Applications

    • Robert B. Burckel
    Pages 397-456
  8. Convergent Sequences of Holomorphic Functions

    • Robert B. Burckel
    Pages 457-527
  9. The Riemann Mapping Theorem

    • Robert B. Burckel
    Pages 585-665
  10. Simple and Double Connectivity

    • Robert B. Burckel
    Pages 667-712
  11. Isolated Singularities

    • Robert B. Burckel
    Pages 713-827
  12. Omitted Values and Normal Families

    • Robert B. Burckel
    Pages 829-897
  13. Back Matter

    Pages 898-1123

About this book

This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail.  Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and rigor.  Standard and novel proofs are explored in unusual detail, and exercises – many with helpful hints – provide ample opportunities for practice and a deeper understanding of the material.

In addition to the mathematical theory, the author also explores how key ideas in complex analysis have evolved over many centuries, allowing readers to acquire an extensive view of the subject’s development.  Historical notes are incorporated throughout, and a bibliography containing more than 2,000 entries provides an exhaustive list of both important and overlooked works.  


Classical Analysis in the Complex Plane will be a definitive reference for both graduate students and experienced mathematicians alike, as well as an exemplary resource for anyone doing scholarly work in complex analysis.  The author’s expansive knowledge of and passion for the material is evident on every page, as is his desire to impart a lasting appreciation for the subject.




“I can honestly say that Robert Burckel’s book has profoundly influenced my view of the subject of complex analysis.  It has given me a sense of the historical flow of ideas, and has acquainted me with byways and ancillary results that I never would have encountered in the ordinary course of my work.  The care exercised in each of his proofs is a model of clarity in mathematical writing…Anyone in the field should have this book on [their bookshelves] as a resource and an inspiration.”
- From the Foreword by Steven G. Krantz

Authors and Affiliations

  • Department of Mathematics, Kansas State University, Manhattan, USA

    Robert B. Burckel

About the author

Robert B. Burckel is Professor Emeritus of Mathematics at Kansas State University.

Bibliographic Information

Buy it now

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access