Synopses & Reviews
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 für 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
Review
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.
Synopsis
One of the most useful and beautiful branches of mathematics is the classical theory of analytic functions. Using a unique approach that employs special functions and hands-on calculus methods, Complex Analysis provides an excellent treatment of the subject. Well-written with thought-provoking remarks and driven by examples and interesting problems, the book is geared towards several math disciplines including number theory, mathematical physics, and statistics.
Synopsis
The classical theory of one complex variable is taught in universities throughout the world. The introduction is concise but by no means superficial, and is based on the premise that "anything worth doing is worth doing with interesting examples". This book is filled with techniques and examples rather than only definitions and theorems.
Synopsis
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.
Synopsis
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.
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.