, This book helps students understand and You have conquered this course when you
solve the most fundamental problems in can solve these eight linear equations.
differential equations and linear algebra. First order
dy/dt = ay
Differential equations Matrix equations dy/dt = ay + q
Continuous problems Discrete problems Second order
Systems in motion Systems at rest d2 y/dt2 + Bdy/dt + Cy= O
dy/dt = Ay + q Ay = b and Ax = h d2 y/dt2 + Bdy/dt + Cy= q
First order systems
dy/dt = Ay
Yparticular dy/dt = Ay + q
Ycomplete
Second order systems
Ynullspace
d2 y/dt2 + Sy = O
d2 y/dt2 + Sy = q
Ayp=b
A{fp+Yn)=b Advanced problems
Ayn =0 Nonlinear dy/dt = f(t,y)
Heat eqn 8u/ 8t = a2u/8x 2
Wave eqn 8 2 u/8t2 = 8 2 u/8x 2
dyp /dt = Ayp + q
dy/dt = Ay + q
Differential equations and linear algebra
dyn /dt = Ay n
are the heart of undergraduate mathematics.
I I I I I 1 1 1 1 1 1 1 1 i illnlll 1
ISBN 978-0-9802327-9-0
,DIFFERENTIAL EQUATIONS
AND
LINEAR ALGEBRA
GILBERT STRANG
Department of Mathematics
Massachusetts Institute of Technolo
l
, 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.
m'E;X typesetting by Ashley C. Fernandes ()
Printed in the United States of America
Other texts from Wellesley - Cambridge Press
Introduction to Linear Algebra, 5th Edition (2016) Gilbert Strang 978-0-9802327-7-6
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, Third edition (2017) 978-0-9802327-5-2
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 math.mit.edu/ �gs
Wellesley MA 02482 USA phone(781) 431-8488
www.wellesleycambridge.com 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
That site links to video lectures on this book by Gilbert Strang and Cleve Moler.
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 Gorn;:alo Morais. This is
the first example of chaos, found by Edward Lorenz.
The cover was designed by Lois Sellers and Gail Corbett.
solve the most fundamental problems in can solve these eight linear equations.
differential equations and linear algebra. First order
dy/dt = ay
Differential equations Matrix equations dy/dt = ay + q
Continuous problems Discrete problems Second order
Systems in motion Systems at rest d2 y/dt2 + Bdy/dt + Cy= O
dy/dt = Ay + q Ay = b and Ax = h d2 y/dt2 + Bdy/dt + Cy= q
First order systems
dy/dt = Ay
Yparticular dy/dt = Ay + q
Ycomplete
Second order systems
Ynullspace
d2 y/dt2 + Sy = O
d2 y/dt2 + Sy = q
Ayp=b
A{fp+Yn)=b Advanced problems
Ayn =0 Nonlinear dy/dt = f(t,y)
Heat eqn 8u/ 8t = a2u/8x 2
Wave eqn 8 2 u/8t2 = 8 2 u/8x 2
dyp /dt = Ayp + q
dy/dt = Ay + q
Differential equations and linear algebra
dyn /dt = Ay n
are the heart of undergraduate mathematics.
I I I I I 1 1 1 1 1 1 1 1 i illnlll 1
ISBN 978-0-9802327-9-0
,DIFFERENTIAL EQUATIONS
AND
LINEAR ALGEBRA
GILBERT STRANG
Department of Mathematics
Massachusetts Institute of Technolo
l
, 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.
m'E;X typesetting by Ashley C. Fernandes ()
Printed in the United States of America
Other texts from Wellesley - Cambridge Press
Introduction to Linear Algebra, 5th Edition (2016) Gilbert Strang 978-0-9802327-7-6
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, Third edition (2017) 978-0-9802327-5-2
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 math.mit.edu/ �gs
Wellesley MA 02482 USA phone(781) 431-8488
www.wellesleycambridge.com 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
That site links to video lectures on this book by Gilbert Strang and Cleve Moler.
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 Gorn;:alo Morais. This is
the first example of chaos, found by Edward Lorenz.
The cover was designed by Lois Sellers and Gail Corbett.
