Ordinary Differential Equations Mathematical Tools for Physicists
This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE ). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen
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Ordinary Differential Equations Mathematical Tools for Physicists
Ordinary Differential Equations
Raza Tahir-Kheli
Ordinary Differential Equations Mathematical Tools for Physicists
123
Raza Tahir-Kheli Department of Physics Temple University Philadelphia, PA, USA
ISBN 978-3-319-76405-4 ISBN 978-3-319-76406-1 https://doi.org/10.1007/978-3-319-76406-1
(eBook)
Library of Congress Control Number: 2018933457 © Springer Nature Switzerland AG 2018 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to my friends Sir Roger J. Elliott, Kt., F.R.S. (in Memorium) Sir Anthony J.Leggett, KBE, F.R.S., Nobel Laureate Alan J. Heeger, Nobel Laureate J. Robert Schrieffer, Nobel Laureate my wife Ambassador Shirin Raziuddin Tahir-Kheli and our grandchildren Taisiya, Alexander, Cyrus, Gladia
Preface
This book is intended as a reader-friendly source for self-study and as an accessible textbook that contains many solved problems. My experience teaching at Temple University the mathematical physics course that includes ordinary differential equations has guided the writing of this textbook. The mathematical physics course is offered to undergraduates in their pre- or final year of study in physics, engineering, chemistry, earth and environmental sciences, or mathematical biology. It is also taken by beginning graduate students working toward a master’s degree. Years of teaching have helped me understand what works for students and what does not. In particular, I have learned that the more attention a student pays to taking notes, the less he/she understands of the subject matter of the lecture being delivered. Further, I have noticed that when, a week in advance of the delivery of the lecture, a stude
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