Skip to main content
SpringerLink
Log in
Birkhäuser

Complex Analysis

Fundamentals of the Classical Theory of Functions

  • Textbook
  • © 1998

Overview

Authors:
  1. John Stalker

    1. Department of Mathematics, Princeton University, Princeton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • An affordable softcover edition of a classic text
  • May be used as a textbook or as a self-study guide
  • Includes beautiful illustrations, a rich set of examples of key concepts, numerous exercises
  • Excellent bibliography and index
  • Includes supplementary material: sn.pub/extras

Part of the book series: Modern Birkhäuser Classics (MBC)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Special Functions

    • John Stalker
    Pages 1-76

  3. Analytic Functions

    • John Stalker
    Pages 77-147

  4. Elliptic and Modular Functions

    • John Stalker
    Pages 149-199

  5. A Quick Review of Real Analysis

    • John Stalker
    Pages 201-220

  6. Back Matter

    Pages 221-228
    Download chapter PDF
Back to top

Keywords

About this book

All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy­ sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse­ quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com­ plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.

Reviews

From the reviews:

The first chapter deals with a beautiful presentation of special functions... The third chapter covers elliptic and modular functions...in much more detail, and from a different point of view, than one can find in standard introductory books... For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference.

---Mathematical Reviews

Mainly original papers are cited to suppoert the historical remarks. The book is well readable.

---ZentralblattMATH

This is an unusual textbook, incorporating material showing how classical function theory can be used.  The general scheme is to show the reader how things were developed without following the traditional approach of most books on functional theory. This book can be recommended to those who like to see applications of the theory taught in "classical courses".

---EMS

“The intended audience for this book is anyone who has taken a calculus course, who knows or is willing to believe the elementary theorems of real analysis given in the appendix, and who wants to learn the classical theory of analytic functions. … The book is easy to read and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference.” (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1188, 2010)

Authors and Affiliations

  • Department of Mathematics, Princeton University, Princeton, USA

    John Stalker

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation