Differential Equations For Scientists and Engineers
This book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, incl
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Differential Equations For Scientists and Engineers
Differential Equations
Allan Struthers • Merle Potter
Differential Equations For Scientists and Engineers Second Edition
123
Allan Struthers Department of Mathematical Sciences Michigan Technological University Houghton, MI, USA
Merle Potter Okemos, MI, USA
ISBN 978-3-030-20505-8 ISBN 978-3-030-20506-5 (eBook) https://doi.org/10.1007/978-3-030-20506-5 © Springer Nature Switzerland AG 2019 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
Preface In Differential Equations for Scientists and Engineers, we endeavor to introduce students to two interesting and important areas of mathematics that enjoy powerful interconnections and applications. The text presents an introduction to linear algebra and then in its remaining six chapters investigates differential equations while highlighting the role that linearity plays in their study. Throughout the text, we strive to reach the following goals: • To motivate the study of linear algebra and differential equations through interesting applications in order that students may see how theoretical results can answer fundamental questions that arise in physical situations. • To demonstrate the fact that linear algebra and differential equations can be presented as two parts of a mathematical whole that is coherent and interconnected. Indeed, we regularly discuss how the structure of solutions to linear differential equations and systems of equations exemplify important ideas in linear algebra and how linear algebra often answers key questions regarding differential equations. • To present an exposition that is intended to be read and understood by students. While certainly every textbook is written wi
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