Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (7 chapters)
Keywords
About this book
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. FedorovskiÄ, 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)
Authors and Affiliations
Bibliographic Information
Book Title: Green's Functions and Infinite Products
Book Subtitle: Bridging the Divide
Authors: Yuri A. Melnikov
DOI: https://doi.org/10.1007/978-0-8176-8280-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LCC 2011
Hardcover ISBN: 978-0-8176-8279-8Published: 31 August 2011
eBook ISBN: 978-0-8176-8280-4Published: 30 August 2011
Edition Number: 1
Number of Pages: X, 165
Number of Illustrations: 32 b/w illustrations
Topics: Analysis, Ordinary Differential Equations, Partial Differential Equations, Applications of Mathematics