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This book originated from my class notes for teaching Math 286, differential equations, at the University of Illinois at Urbana-Champaign in fall 2008 and spring 2009. It is a first course on differential 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, Differential 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 Differential Equations [I], Stanley Farlow’s Differential Equations and Their Applications [F], which is now available from Dover, Berg and McGregor’s Elementary Partial Differential Equations [BM], and Boyce and DiPrima’s Elementary Differential 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 (http://www.math.uiuc.edu/iode/). 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 http://www.jirka.org/genius.html). I have used Genius in class to show these (and other) graphs.
This book is available from http://www.jirka.org/diffyqs/. Check there for any possible updates or errata. The LATEX 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, Jeff 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 Shin, Gladys Cruz, Jonathan Gomez, Janelle Louie, Navid Froutan, Grace Victorine, Paul Pearson, Jared Teague, Ziad Adwan, Martin Weilandt, Sönmez Şahutoğlu, 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:
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 be dropped, while still covering chapters 4 and 5. The textbook was originally done for two types of courses. Either at 4 hours a week for a semester (Math 286 at UIUC):
Introduction, chapter 1, chapter 2, chapter 3, chapter 4 (w/o § 4.10), chapter 5 (or 6 or 7).
Or a shorter version (Math 285 at UIUC) of the course at 3 hours a week for a semester:
Introduction, chapter 1, chapter 2, chapter 4 (w/o § 4.10), (and maybe chapter 5, 6, or 7).
The complete book can be covered in approximately 65 lectures, that of course depends on the lecturers speed and does not account for exams, review, or time spent in computer lab (if for example using IODE). Therefore, a two quarter course can easily be run with the material, and if one goes a bit slower than I do, then even a two semester course.
The chapter on Laplace transform (chapter 6), the chapter on Sturm-Liouville (chapter 5), and the chapter on power series (chapter 7) are more or less interchangeable time-wise. If time is short the first two sections of the chapter on power series (chapter 7) make a reasonable self-contained unit.