An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See the book webpage (see inside) for more information, updates, errata, and a list of classroom adoptions.
Very, very useful as a supplemental text. And, it's open source, which means it is not only free (the author's website is a google away) but also remixable - meaning, you are free to create and distribute your own version of the text under a creative commons license (http://creativecommons.org/licenses/b...) as long as you do so under the same license as the original. So far none of my students has taken advantage of this flexibility, but they do appreciate the clarity in Lebl's explanations. As do I, frankly. Some good choices are made as to what is left out - for example, one does not need the Wronskian to show that two functions are linearly independent.
I say that this is useful as a supplemental text. It would not work as a primary text for the course I teach. There are not enough exercises (although the ones there are are nice, and I have assigned some of them, even though our main book has more). Some topics that are on my syllabus are not covered here. Nevertheless, I appreciate having this resource.