Excerpts from book:

These are introductory notes on ordinary and partial differential equations. Assumed background is calculus and a little physics. Linear algebra is not assumed, and is introduced here in four of the lectures. Those four lectures have been used in the Engineering Mathematics course at Cornell University for several years. The notes as a whole have not been used as a text, but have been freely available for many years from the author's web page. The notes as written are quite close to lectures the author has delivered while attempting to explain various textbooks to his students.

The notes contain about one third of the material of the typical differential equations book, and are therefore concerned with only the most important ideas. The style of the notes is approximately that of the author's lectures, in that most ideas are taught by example, and that the ideas as being at least as important as the calculations. For fuller coverage, see any of the excellent books:

1. Agnew, Ralph Palmer, Differential Equations, McGraw-Hill, 1960
2. Hubbard, John H., and West, Beverly H., Differential Equations, a Dynamical Systems Approach, Parts 1 and 2, Springer, 1995 and 1996
3. Churchill, Ruel V., Fourier Series and Boundary Value Problems, McGraw Hill, 1941

Some of the exercises have the format What's wrong with this? .... ?!? Most of these are errors taken from test papers of students in this class, so it could be quite beneficial to study them.