Complex Analysis - John Stalker

Complex Analysis

Fundamentals of the Classical Theory of Functions

(Autor)

Buch | Hardcover
242 Seiten
1998
Birkhauser Boston Inc (Verlag)
978-0-8176-4038-5 (ISBN)
64,09 inkl. MwSt
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In this concise introduction to the classical theory of one complex variable the content is driven by techniques and examples, rather than definitions and theorems.
This clear, concise introduction to the classical theory of one complex variable is based on the premise that "anything worth doing is worth doing with interesting examples." The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course. "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 support the historical remarks. The book is well readable."
(Zentralblatt fur Mathematik) "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)

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.

Erscheint lt. Verlag 19.5.1998
Zusatzinfo black & white illustrations
Verlagsort Secaucus
Sprache englisch
Maße 155 x 235 mm
Gewicht 520 g
Einbandart gebunden
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Analytic Functions • Bernoulli Polynomials • Biquadratic Reciprocity • Cauchy Integral Formula • complex multiplication • Contour Integration • Einstein series • elliptic functions • Euler-MacLaurin Summation • hypergeometric function • lattices • Mellin-Barnes Integrals • Metamorphic Functions • Quadratic Reciprocity • Real analysis • rigidity • Stirling's Series • Whittaker Function
ISBN-10 0-8176-4038-X / 081764038X
ISBN-13 978-0-8176-4038-5 / 9780817640385
Zustand Neuware
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