Introduction to Differential Equations

Math 204 at UVic consists of a Vector Calculus portion followed by Ordinary Differential Equations (ODEs). This book covers the ODE portion, while this separate Vector Calculus "Book"¹ supports the Vector Calculus portion.

The original version of the textbook by Jiří Lebl comes in three forms:

Additionally, Jiří Lebl’s website for the book⁵ contain’s a lot of additional information including the source code.

Note that this forked version of the book for Math 204 at UVic is only available in web version. If you would prefer a .pdf or printed version, you can access the original .pdf or printed version with the above links. See the next section for differences between the versions.

If you are an instructor, please consult the original version of the text⁶ for more information and potential uses.

As of this writing, the original text by Jiří Lebl and the forked version by Trefor Bazett are very similar. The most substantial changes in the forked version are embedding of a video series by Trefor Bazett and an expansion of the exercises at the end of each section, with more questions, more answers, and some brief solutions. Additioally, there is a rearrangement of the content. For a more precise comparison, please consult the respective github pages for the original and forked version.

A few chapters in this book are not taught in Math 204, namely Systems, Non-Linear Systems, Eigenvalue Systems, and PDEs. These chapters remain for reference purposes in the forked version of the textbook entirely untouched by Trefor Bazett.

The full playlist of videos by Trefor Bazett can be found here⁷, and consists of both Vector Calculus (embedded in the Vector Calculus "Book"⁸) and ODEs (embedded throughout this book).

The videos are intended to be complimentary to the textbook. You could learn the content just by reading the textbook, as in the original version by Lebl. The other direction is not true; the videos alone don’t always cover all the content. Typically the videos use slightly different examples from the textbook so that you can get extra exposure by reading/watching both. While there was an effort for the notation and scope of the videos to be similar to the textbook, ultimately the book is largely written by Lebl and the videos recorded by Bazett and there are stylistic differences and differences in emphasis between these two. Typically videos are placed immediately prior to the analogous text content covered in the video.

Note that the videos used in this text are one Trefor Bazett’s UVic-specific channel @DrTreforUVic⁹. Trefor Bazett also maintains a public YouTube channel which contain versions of the same videos. In general the videos embedded from the @DrTreforUVic channel are a cleaner learning experience as they are not monetized and contain no calls-to-action (eg: Like and Subscribe!).

The book’s website https://www.jirka.org/diffyqs/¹⁰ contains the following resources:

Jiří Lebl taught the UIUC courses using IODE (https://faculty.math.illinois.edu/iode/¹¹). IODE is a free software package that works with Matlab (proprietary) or Octave (free software). The graphs in the book were made with the Genius software (see https://www.jirka.org/genius.html¹²).

The LaTeX source is available on github for the original version by Lebl (https://github.com/jirilebl/diffyqs¹³) as well as the forked version by Bazett (https://github.com/tbazett/diffyqs¹⁴) for possible modification and customizations.

Acknowlegements by Trefor Bazett: Firstly, I want to thank the incredibly work of Jiří Lebl for creating and maintaining this excellent textbook, without which this project would have been beyond daunting to begin. I want to thank both Muhammad Awais and Afif Omar for their extensive work on revising the exercises, answers, and solutions. This project is supported by a grant through the LTSI at the University of Victoria to create Open Educational Resources.

Acknowledgements by Jiří Lebl: Firstly, I would like to acknowledge Rick Laugesen. I used his handwritten class notes the first time I taught Math 286. My organization of this book through chapter 5, and the choice of material covered, is heavily influenced by his 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, Simon Tse, Andrew Browning, James Choi, Dusty Grundmeier, John Marriott, Jim Kruidenier, Barry Conrad, Wesley Snider, Colton Koop, Sarah Morse, Erik Boczko, Asif Shakeel, Chris Peterson, Nicholas Hu, Paul Seeburger, Jonathan McCormick, David Leep, William Meisel, Shishir Agrawal, Tom Wan, Andres Valloud, and probably others I have forgotten. Finally, I would like to acknowledge NSF grants DMS-0900885 and DMS-1362337.