Complex Analysis: Fundamentals of the Classical Theory of Functions

Author:   John Stalker
Publisher:   Birkhauser Boston Inc
ISBN:  

9780817640385


Pages:   242
Publication Date:   19 May 1998
Format:   Hardback
Availability:   Out of print, replaced by POD   Availability explained
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Complex Analysis: Fundamentals of the Classical Theory of Functions


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Overview

"The classical ""theory of complex variable"" is considered by some as one of the most beautiful and useful subjects in mathematics. This concise introduction is based on the premise that ""anything worth doing is worth doing with interesting examples"". Content is driven by techniques rather than by definitions and theorems. Examples are chosen from the analytic theory of numbers and classical special functions, but while they are mostly geared towards number theory, mathematical physics, the techniques are generally applicable. Prerequisites are a standard course in calculus."

Full Product Details

Author:   John Stalker
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.520kg
ISBN:  

9780817640385


ISBN 10:   081764038
Pages:   242
Publication Date:   19 May 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of print, replaced by POD   Availability explained
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Preface.- Outline.- Special Functions.- 1.1 The Gamma Function.- 1.2 The Distribution of Primes I.- 1.3 Stirling's Series.- 1.4 The Beta Integral.- 1.5 The Whittaker Function.- 1.6 The Hypergeometric Function.- 1.7 Euler-MacLaurin Summation.- 1.8 The Zeta Function.- 1.9 The Distribution of Primes II.- 2 Analytic Functions.- 2.1 Contour Integration.- 2.2 Analytic Functions.- 2.3 The Cauchy Integral Formula.- 2.4 Power Series and Rigidity.- 2.5 The Distribution of Primes III.- 2.6 Meromorphic Functions.- 2.7 Bernoulli Polynomials Revisited.- 2.8 Mellin-Barnes Integrals I.- 2.9 Mellin-Barnes Integrals II.- 3 Elliptic and Modular Functions.- 3.1 Theta Functions.- 3.2 Eisenstein Series.- 3.3 Lattices.- 3.4 Elliptic Functions.- 3.5 Complex Multiplication.- 3.6 Quadratic Reciprocity.- 3.7 Biquadratic Reciprocity.- A Quick Review of Real Analysis.- Bibliography.- Index.

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 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. <p>--Mathematical 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


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