Green's Functions and Infinite Products

Bridging the Divide

Authors: Melnikov, Yuri A.

  • Includes new material on the connection between Green's functions and infinite products
  • Every chapter begins with a review guide outlining the basic concepts covered in the chapter
  • A set of carefully designed challenging exercises is available at the end of each chapter
  • Hints, comments and answers to most of those exercises can be found at the end of the text
  • Several illustrative examples are offered at the end of most sections
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  • ISBN 978-0-8176-8280-4
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  • Immediate eBook download after purchase
Hardcover $59.95
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  • ISBN 978-0-8176-8279-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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About this Textbook

This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems.

Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.

Reviews

From the reviews:

“The book under review is an interesting textbook which is intended for students (both undergraduate and postgraduate) specializing in pure and applied mathematics. It may be considered as a good complement to standard courses in analysis and differential equations.” (Konstantin Yu. Fedorovskiĭ, Mathematical Reviews, May, 2013)

“The present book provides an introduction to some recent research of the author based on a method for deriving infinite product representations for the Green’s functions of the two-dimensional Laplace equation on certain domains. … The book contains ample background material on infinite products and Green’s functions … and is, hence, accessible for graduate students. In particular, the presentation is clear and self-contained.” (G. Teschl, Monatshefte für Mathematik, Vol. 166 (3-4), June, 2012)

“This book is devoted to some new infinite products for trigonometric and hyperbolic functions. … the infinite products investigated in the book have the same speed of convergence as the classical ones. … The book is written on a very comprehensive level and can be useful for students studying equations of mathematical physics and computer modeling.” (Yana Kinderknecht, Zentralblatt MATH, Vol. 1235, 2012)


Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-8176-8280-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-0-8176-8279-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Green's Functions and Infinite Products
Book Subtitle
Bridging the Divide
Authors
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LCC
eBook ISBN
978-0-8176-8280-4
DOI
10.1007/978-0-8176-8280-4
Hardcover ISBN
978-0-8176-8279-8
Edition Number
1
Number of Pages
X, 165
Number of Illustrations and Tables
32 b/w illustrations
Topics