Generalized Fourier Series

There are many methods for computing approximate solutions of two-dimensional elliptic boundary value problems, each with its advantages and disadvantages. Thus, the finite difference and finite element techniques have the ability to generate the approxim

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Christian Constanda Dale Doty

The Generalized Fourier Series Method Bending of Elastic Plates

Developments in Mathematics Volume 65

Series Editors Krishnaswami Alladi, Department of Mathematics, University of Florida, Gainesville, FL, USA Pham Huu Tiep, Department of Mathematics, Rutgers University, Piscataway, NJ, USA Loring W. Tu, Department of Mathematics, Tufts University, Medford, MA, USA

Aims and Scope The Developments in Mathematics (DEVM) book series is devoted to publishing well-written monographs within the broad spectrum of pure and applied mathematics. Ideally, each book should be self-contained and fairly comprehensive in treating a particular subject. Topics in the forefront of mathematical research that present new results and/or a unique and engaging approach with a potential relationship to other fields are most welcome. High-quality edited volumes conveying current state-of-the-art research will occasionally also be considered for publication. The DEVM series appeals to a variety of audiences including researchers, postdocs, and advanced graduate students.

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Christian Constanda • Dale Doty

The Generalized Fourier Series Method Bending of Elastic Plates

Christian Constanda The Charles W. Oliphant Professor of Mathematics Department of Mathematics The University of Tulsa Tulsa, OK, USA

Dale Doty Department of Mathematics The University of Tulsa Tulsa, OK, USA

ISSN 1389-2177 ISSN 2197-795X (electronic) Developments in Mathematics ISBN 978-3-030-55848-2 ISBN 978-3-030-55849-9 (eBook) https://doi.org/10.1007/978-3-030-55849-9 Mathematics Subject Classification: 31A10, 35C15, 35J57, 74K20, 74G15 © Springer Nature Switzerland AG 2020 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, expressed 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. This Springer imprint is published by the registered company Springer Nature Switze