Green's Functions Potential Fields on Surfaces
This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are enga
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Yuri A. Melnikov Volodymyr N. Borodin
Green's Functions Potential Fields on Surfaces
Developments in Mathematics Volume 48
Series editors Krishnaswami Alladi, Gainesville, USA Hershel M. Farkas, Jerusalem, Israel
More information about this series at http://www.springer.com/series/5834
Yuri A. Melnikov Volodymyr N. Borodin •
Green’s Functions Potential Fields on Surfaces
123
Yuri A. Melnikov Department of Mathematical Sciences Middle Tennessee State University Murfreesboro, TN USA
ISSN 1389-2177 Developments in Mathematics ISBN 978-3-319-57242-0 DOI 10.1007/978-3-319-57243-7
Volodymyr N. Borodin Department of Mechanical Engineering Tennessee Technological University Cookeville, TN USA
ISSN 2197-795X (electronic) ISBN 978-3-319-57243-7
(eBook)
Library of Congress Control Number: 2017938130 Mathematics Subject Classification (2010): 34B27, 35J08, 35J15, 35J25, 65N80 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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Preface
Efficiency of the Green’s function instrument is commonly recognized and as a result, its use is frequently recommended in the qualitative analysis of boundary value problems for ordinary as well as partial differential equations. Nowadays, this instrument has been transformed into a powerful investigative tool that has been around for almost two centuries since its introduction by a brilliant British mathematician and physicist, George Green. His elegant elaborations had revealed impressive constructive properties of Green’s functions. It would have been quite a misconception to presume that the realm of implementations of Green’s functions is
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