Notes on Diffy Qs is an introductory textbook on differential equations for engineering students. In approach it is close to (and internally cross-referenced with) books by Edwards and Penney (Differential Equations and Boundary Value Problems) and Boyce and DiPrima (Elementary Differential Equations and Boundary Value Problems). Lebl’s intent is to provide a comparable book in hardcopy at a low cost (or freely available here for download). The hardcopy is entirely in black-and-white whereas the downloadable version has several color illustrations.
The text is intended to support a one-semester or two-quarter course, and could be stretched to two semesters with some supplementary material. The contents are quite standard for a course that aims to introduce both ordinary and partial differential equations. The major topics are first and higher order ordinary differential equations (ODEs), systems of ODEs, then Fourier series and partial differential equations (PDEs), eigenvalue problems (including Sturm-Liouville problems), the Laplace transform and power series methods. Linear algebra is introduced as needed, but is kept to a minimum.
If one considers what knowledge and skills an engineering student should take from an introductory course on differential equations, one might include:
Recognizing common differential equations (e.g., variations of harmonic oscillator equation, heat equation, wave equation);
Understanding basic techniques for solving ODEs and PDEs;
Creating awareness of issues involving existence and uniqueness;
Learning rudiments of qualitative behavior of solutions.
Getting some experience with numerical solutions.
The current text does reasonably well by these criteria. One might wish for some more depth on qualitative methods, and a clearer message that most differential equations do not have closed form solutions.
The writing is plain but clear throughout and the style is relaxed and conversational. Exercises are plentiful but not particularly distinctive. There are plenty of examples, all carefully worked out. Where examples involve applications, these are all (unsurprisingly) in physics or engineering. Yet it might not be a bad idea for engineers to see at least a few applications outside their field.
Overall, this is a very competent — but not especially inspired – introduction to differential equations, one which is sensitive to the needs of engineering students in future coursework.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.