The goal of these differential equations notes is to eventually cover all standard topics in a typical two-semester course sequence in differential equations at the undergraduate level (such courses are often taken by math, engineering, and science majors).


Prerequisites include trigonometry, the differential calculus (derivatives), and the integral calculus (integrals) through integration techniques such as substitution and integration by parts. We will make use of some power series, multivariate calculus, linear algebra, and complex variables, but the necessary concepts will be explained as needed.

Usage Tips

These differential equations notes consist of a series of “digital notecards,” each accompanied by a video explanation. There are at least two ways to use these notes.

  1. You can use the notecards to rapidly review what you’ve already learned, watching the videos only when you cannot provide the correct answer to a notecard’s prompt.
  2. You can learn core topics by watching the videos, and then you can quiz yourself by attempting to answer the prompt on the corresponding notecard. You can do this to learn on your own (in which case I recommend working additional exercises for practice), or to supplement a university course. In the latter case, I recommend watching the videos before your lecture if possible. That way, the lecture will serve as a review session, and you’ll be able to follow it much better!

Course Outline (with links to notes)


Each of the following resources covers most of the topics that will be included in the differential equations notes presented on this site. The first three books have been adopted by many universities for their differential equations courses. However, this is just a sample; there are many other books with similar coverage.