Author | Stalker, John. author |
---|---|

Title | Complex Analysis [electronic resource] : Fundamentals of the Classical Theory of Functions / by John Stalker |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998 |

Connect to | http://dx.doi.org/10.1007/978-0-8176-4919-7 |

Descript | XI, 228 p. online resource |

SUMMARY

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 fรผr 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

CONTENT

Preface. Outline. 1. 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

Mathematics
Functions of complex variables
Mathematics
Functions of a Complex Variable
Several Complex Variables and Analytic Spaces