I’m teaching differential equations next semester, and I’m changing the course in some fundamental ways since the last time I taught it — so much so that I needed a new book for the course. (I’ve ruled out the textbook-free option for this class for reasons I explained here.) After some searching, I ended up going with the Boyce/DiPrima text. But I gained a lot of respect, and found a lot of affection, for Tenenbaum and Pollard’s classic text on the subject from 1963.
First of all, the textbook is a giant brick of a book, loaded with great exposition, clear examples, and challenging problems. And being a Dover paperback, it’s only a measley $16.47 through Amazon. But the thing I love about it, which is something I love about all math and science books from this era, is its tone — clear, precise, tough-minded, and no-nonsense. And yet inviting and enjoyable at the same time. (Which precisely describes what I’d like the students in the course to be.)
A great example is the following quote that appears at the end of a solid review of functions and just before they start looking at differential equations proper. Note that there is no intervening review of calculus between these two sections. That’s because the authors expect students to actually know calculus upon entering the course. They say:
In the calculus course, you learned how to differentiate elementary functions and how to integrate the resulting derivatives. If you have forgotten how, it would be an excellent idea at this point to open your calculus book and review this material. [emph. added]
I actually cheered when I read that. Differential equations is an extension of calculus; calculus is a prerequisite; you had calculus once; so if you forgot how to do it, get off your duff and crack a freaking book. End of story.
It’s the exact opposite of most modern math textbooks that start by assuming that the reader is five years younger and 30 IQ points dumber than s/he really is, and scared witless of math and unable to read past a 5th-grade level on top of that, and which proceeds to hand-hold and touchy-feel its way through whatever subject it is supposedly about. But not so with this book, nor with any other post-Sputnik era math and science books I’ve seen. That softening up seems to have occurred sometime around 1980.
Ironically, this 1963 text is superbly written with great clarity, vivid illustrations to motivate the material, and plenty of useful examples. When books started softening up — supposedly in an attempt to help struggling students — the things that actually help those students such as clarity and completeness actually went away.
I ended up going with the more modern book because I needed more in the way of computer applications (not many of those were around in 1963). But I will be using this Tenenbaum and Pollard text quite a bit, for my own enjoyment if nothing else, and perhaps as a lesson in how to write mathematics clearly.