Differential Equations and Linear Algebra Copyright ©2014 by Gilbert Strang ISBN 978-0-9802327-9-0 All rights reserved. No part of this work may be reproduced or stored or transmitted by any means, including photocopying, without written permission from Wellesley - Cambridge Press. Translation in any language is strictly prohibited. Typeset by Valutone (www.valutone.co.in) Printed in the United States of America Other texts from Wellesley - Cambridge Press Introduction to Linear Algebra, 4th Edition (2009) Gilbert Strang 978-0-9802327-1-4 Computational Science and Engineering, Gilbert Strang 978-0-9614088-1-7 Wavelets and Filter Banks, Gilbert Strang & Truong Nguyen 978-0-9614088-7-9 Introduction to Applied Mathematics, Gilbert Strang 978-0-9614088-0-0 Calculus, Gilbert Strang, Second edition (2010) 978-0-9802327-4-5 Algorithms for Global Positioning, Kai Borre & Gilbert Strang (2012) 978-0-9802327-3-8 Analysis of the Finite Element Method, Gilbert Strang & George Fix 978-0-9802327-0-7 Essays in Linear Algebra, Gilbert Strang 978-0-9802327-6-9 Wellesley - Cambridge Press Box 812060 Wellesley MA 02482 USA www.wellesleycambridge.com diffeqla@gmail.com math.mit.edu/gs phone (781) 431-8488 fax (617) 253-4358 Our books are also distributed by SIAM (in North America) and by Cambridge University Press (in the rest of the world). The website with solutions to problems in this textbook is math.mit.edu/dela Linear Algebra and Differential Equations are on MIT’s OpenCourseWare site ocw.mit.edu. This provides video lectures of the full courses 18.03 and 18.06. Course material is on the teaching website: web.mit.edu/18.06 Highlights of Calculus (17 lectures and text) are on ocw.mit.edu The front cover shows the Lorenz attractor, drawn for this book by Gonçalo Morais. This is the first example of chaos, found by Edward Lorenz. The cover was designed by Lois Sellers and Gail Corbett.