Fluid Dynamics and Linear Elasticity A First Course in Continuum Mec
This book provides a concise introduction to continuum mechanics, with a particular emphasis on fluid dynamics, suitable for upper undergraduate students in applied mathematics and related subjects.Starting with a preliminary chapter on tensors, the main
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Michael S. Ruderman
Fluid Dynamics and Linear Elasticity A First Course in Continuum Mechanics
Springer Undergraduate Mathematics Series Advisory Editors M. A. J. Chaplain, St. Andrews, UK Angus MacIntyre, Edinburgh, UK Simon Scott, London, UK Nicole Snashall, Leicester, UK Endre Süli, Oxford, UK Michael R. Tehranchi, Cambridge, UK John F. Toland, Bath, UK
More information about this series at http://www.springer.com/series/3423
Michael S. Ruderman
Fluid Dynamics and Linear Elasticity A First Course in Continuum Mechanics
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Prof. Michael S. Ruderman School of Mathematics and Statistics University of Sheffield Sheffield, UK
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-030-19296-9 ISBN 978-3-030-19297-6 (eBook) https://doi.org/10.1007/978-3-030-19297-6 Mathematics Subject Classification (2010): 74B05, 74J05, 74J15, 75Bxx, 76Dxx © 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, 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This text is based on an introductory course in Continuum Mechanics given at the University of Sheffield over a period of fifteen years. The main aim of the course, as well as this book, is to give a unified treatment of the topic. I have tried to restrict the required background to that normally familiar to second-year undergraduate mathematics students in the UK. This includes calculus, mathematical analysis, and the basics of the theory of systems of first-order differential equations. I have included a chapter on the theory of tensors since it is commonly used in continuum mechanics but not usually covered in general calculus courses. Its main aim is to introduce tensors and various operations involving them. Tensors a
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