erential equations for engineers. I have also taught Math 285 at UIUC and Math 20D at UCSD
using this book. The standard book for the UIUC course is Edwards and Penney,
Di
↵
erential
Equations and Boundary Value Problems: Computing and Modeling
[
EP
], fourth edition. Some
examples and applications are taken more or less from this book, though they also appear in many
other sources, of course. Among other books I have used as sources of information and inspiration
are E.L. Ince’s classic (and inexpensive)
Ordinary Di
↵
erential Equations
[
I
], Stanley Farlow’s
Di
↵
erential Equations and Their Applications
[
F
], which is now available from Dover, Berg and
McGregor’s
Elementary Partial Di
↵
erential Equations
[
BM
], and Boyce and DiPrima’s
Elementary
Di
↵
erential Equations and Boundary Value Problems
[
BD
]. See the Further Reading chapter at the
end of the book.
I taught the UIUC courses with the IODE software (
).
IODE is a free software package that is used either with Matlab (proprietary) or Octave (free
software). Projects and labs from the IODE website are referenced throughout the book. They need
not be used for this course, but I recommend using them. The graphs in the book were made with
the Genius software (see
). I have used Genius in class to
show these (and other) graphs.
This book is available from
. Check there for any possible
updates or errata. The L
A
T
E
X source is also available from the same site for possible modification
and customization.
I would like to acknowledge Rick Laugesen. I have used his handwritten class notes the first
time I taught Math 286. My organization of this book, and the choice of material covered, is heavily
influenced by his class notes. Many examples and computations are taken from his notes. I am also
heavily indebted to Rick for all the advice he has given me, not just on teaching Math 286. For
spotting errors and other suggestions, I would also like to acknowledge (in no particular order): John
P. D’Angelo, Sean Raleigh, Jessica Robinson, Michael Angelini, Leonardo Gomes, Je
↵
Winegar,
Ian Simon, Thomas Wicklund, Eliot Brenner, Sean Robinson, Jannett Susberry, Dana Al-Quadi,
Cesar Alvarez, Cem Bagdatlioglu, Nathan Wong, Alison Shive, Shawn White, Wing Yip Ho, Joanne
5

6
INTRODUCTION
Shin, Gladys Cruz, Jonathan Gomez, Janelle Louie, Navid Froutan, Grace Victorine, Paul Pearson,
Jared Teague, Ziad Adwan, Martin Weilandt, Sönmez ¸Sahuto˘glu, Pete Peterson, Thomas Gresham,
Prentiss Hyde, Jai Welch, and probably others I have forgotten. Finally I would like to acknowledge
NSF grant DMS-0900885.
The organization of this book to some degree requires that chapters are done in order. Later
chapters can be dropped. The dependence of the material covered is roughly:
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 6
Chapter 7
Chapter 4
Chapter 5
There are some references in chapters 4 and 5 to material from chapter 3 (some linear algebra),
but these references are not absolutely essential and can be skimmed over, so chapter 3 can safely