Differential Equations: Theory and Applications
The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but a
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David Betounes
Differential Equations: Theory Hand Applications Second Edition
David Betounes Department of Physics, Astronomy and Geosciences Valdosta State University 1500 N. Patterson Street Valdosta, GA 31698 USA
Additional material to this book can be downloaded from http://extra.springer.com
ISBN 978-1-4419-1162-9 e-ISBN 978-1-4419-1163-6 DOI 10.1007/978-1-4419-1163-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009938714 Mathematics Subject Classification (2000): 34A34, 34A30, 34A12, 34D05, 34D20, 70E15, 70H05, 70H06, 70H15 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. Historically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathematics, the material is organized so that the book can also be used in a wider setting within today’s modern university and society (see “Ways to Use the Book” below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the instructor’s or reader’s preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend together the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab. The electronic material for mastering and enjoying the computer component of this book is on Springer’s website.
Ways to Use
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