Notes on Diffy Qs: Differential Equations for Engineers

By: Jiří Lebl (website #1 http://www.jirka.org/ (personal), website #2 http://www.math.uiuc.edu/~jlebl/ (work: uiuc), email: jiri...@gmail.com)

Jump to: [Download the book] [Buy paperback] [Web version]

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to Edwards and Penney, Differential Equations and Boundary Value Problems. I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign.

Sample Dirichlet problem solution The aim is to provide a low cost, redistributable, not overly long, high quality textbook that students will actually keep rather than selling back after the semester is over. Even if the students throw it out, they can always look it up on the net again. You are free to have a local bookstore or copy store make and sell copies for your students. See below about the license.

Another reason is to allow modification and customization for a specific purpose if necessary. If you do modify these notes, make sure to mark them prominently as such to avoid confusion. This aspect is also important for longevity of the book. The book can be updated and modified even if I happen to drop off the face of the earth. You do not have to depend on any publisher being interested as with traditional textbooks.

While the textbook may be used by itself, it is can also be used in conjunction with the IODE software. IODE is a free software package for experimenting with basic ODEs developed at University of Illinois specifically for teaching this course. IODE works with both Matlab (proprietary) and Octave (free). The IODE website has several extra projects for the students to work through as homework. The graphs in the book are done using the Genius software.

Temperatures of object with ambient temperature oscillating Table of contents:
Introduction
1. First order ODEs
2. Higher order linear ODEs
3. Systems of ODEs
4. Fourier series and PDEs
5. Eigenvalue problems
6. The Laplace transform

Please let me know at jiri...@gmail.com if you find any typos or have corrections, extra exercises or material, or any other comments. I will always keep all older versions available for download, at least when there are nontrivial updates. When the updates are reasonably minor, I will try to preserve pagination and numbering of sections/examples/theorems/equations/exercises as much as possible.

Do let me know (jiri...@gmail.com) if you use the book for teaching a course!

Download:
One big PDF
(March 7th, 2010, 252 pages, approximately 2MB download)

Look at the errata in the current revision.

Look at the change log to see what changed in the newest version (You can download source files of old versions if you wish).

I am currently teaching Math 285 with these notes, so I expect to make lots of small (and perhaps some not so small) changes and fixes to the manuscript. I am uploading updated versions every time a reasonable number of changes piles up.

Note: There used to be two versions of the notes, one with extra big references to the section names in EP (Edwards-Penney). I don't make a pdf of that version any more. You can make it by editting the source.

Buy paperback: Buy a copy at lulu.com for $14.93. I get $2.50, so by buying a copy you will support this project. You will also save your toner cartridge. This copy is the March 7th, 2010 revision.

Web version: Browse the HTML version of the notes (for easier reading of the notes on the web). The PDF version is still the canonical version however. Some things may look strange or may be hard to read in the web version simply because of imperfections in the conversion.

Source: LaTeX source as a tarball. The main file is diffyqs.tex. I compile the pdf with pdflatex. You also want to run makeindex to generate the index (I generally run pdflatex diffyqs three times, then makeindex diffyqs, and then finally pdflatex diffyqs again). The setup file with all the preamble you may want to edit is diffyqssetup.sty.

License: This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. You can use, print, copy, and share these notes as much as you want. You can base your own notes on these and reuse parts if you keep the license the same. If you plan to use these notes commercially (sell them for more than just production cost) then you need to contact me and we will work something out. If you are printing a course pack for your students then it is fine if the copy service or bookstore is charging a fee for printing and selling the printed copy. I consider that production cost.

Integrating factor formula Useful links:

Department of Mathematics
College of Liberal Arts and Sciences
University of Illinois at Urbana-Champaign
273 Altgeld Hall, MC-382
1409 W. Green Street, Urbana, IL 61801 USA
Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576