One of the overwhelming things about the Internet (to me, at least) is just trying to keep track of what’s out there. With this post, I invite readers to contribute to a list of free (and where fitting, open) calculus texts that are available on the web; I’ve added two that are very low cost (under $20 per student). If people want to offer testimonials or other observations in the comments, that would be especially appreciated.

As noted in an earlier post, there are a couple of calculus texts posted online as part of the American Institute of Mathematics’s Open Textbook Project (those by Strang and Guichard, respectively). Again, Strang’s book is free, but not open, while Guichard’s is open.

Here are some others. The first two have some modest costs associated with them; the remaining ones are all free. None of these, to my knowledge, is open source.

- David Massey, Worldwide Differential Calculus. Massey is the founder of the Worldwide Center of Math; I believe that originally, this text was free. Massey now charges $10 for the .pdf, or $30 for a bound copy. In reviewing earlier versions (when it was posted online), I was struck by how complete the text is (differential calculus is 565 pages!), and how vast the included resources are for students, with even lengthy video tutorials. So not free, but not $189.95 either. Massey’s site has a growing collection of similar books.
- David Smith and Lang Moore, Calculus: Modeling and Application. I was (am) a huge fan of the print version (1st edition) of this text. Smith and Moore have converted the text to an entirely .html platform. Now hosted and endorsed by the MAA, schools can purchase a license agreement to gain access to the full text online for their students. From the order form on the page, it costs roughly $15-$20 per student, depending on the number of students enrolled. This is a great, low-cost alternative, and again the text and materials are extremely high quality. I’m not as big a fan of the .html format and how each link leads to a new window, but I do see advantages of this format.
- Miklos Bona and Sergei Shabanov, Concepts in Calculus I. “From the University of Florida Department of Mathematics, this is the first volume in a three volume presentation of calculus from a concepts perspective.” The other two volumes (for integral and multivariable calculus) are available from the Florida Digital Repository. At under 200 pages, this is a nice, comprehensive introduction to standard concepts in calculus. Exercises are included. Text is free and in .pdf format. (As an aside, the Florida Digital Repository seems to be one of the better online “warehouses” for free texts with a reasonably good search feature.)
- William Smith, The Calculus. Free, but copyrighted (the author doesn’t want any of the text even copied to other locations). The typesetting is poor and hard to read online, and the text has two unusual features (as noted by the author): (a) proofs for everything are included, and (b) the text introduces ideas in one and two variables simultaneously.
- Dan Sloughter, Difference Equations to Differential Equations. Clearly the author has more in mind than calculus, but there’s quite a lot of calculus content available; the table of contents is presented in html, with the links leading the reader to .pdf files that are essentially short individual chapters. Sloughter also offers Yet Another Calculus Text, written from the perspective of the hyperreal numbers.
- Jerome Keisler has a text that seems similar in spirit to Sloughter’s, using infinitesimals, titled Elementary Calculus: an Infinitesimal Approach.
- Paul Garrett, Calculus Refresher. A brief (approximately 80 page) review of some key calculus ideas (with some exercises). This book seems designed for students who’ve had calculus and need some review, rather than for students encountering the ideas for the first time.

What am I missing? Are there other good texts out there that people have used? Testimonials for any of the above?

Here are a few more:

Whitman Calculus [https://sites.google.com/site/whitmanmathematics/] by David Guichard. Full calculus sequence, contains exercises, free PDF.

Funny Little Calculus Text [http://www.math.upenn.edu/~ghrist/FLCT/index.html] by Robert Ghrist. Currently only first semester calculus, very short, no exercises, free PDF.

Paul’s Online Math Notes [http://tutorial.math.lamar.edu/] by Paul Dawkins. Calculus 1-3, Linear Algebra, and more. Free HTML-based material, no exercises, very popular with students.

Differential Calculus with Sage [http://wdjoyner.com/teach/calc1-sage/] by David Joyner and Granville. First semester calculus, incorporates Sage [http://sagemath.org], open-source, free PDF/HTML, includes exercises.

Integral Calculus with Sage [http://boxen.math.washington.edu/home/wdj/teaching/calc2-sage/] by Stein, Hoffman, Joyner, and Minh. Picks up where the previous book left off.

Dover books are pretty inexpensive.

Calculus: An Intuitive and Physical Approach, by Morris Kline may be a good book for some students. At $27 for 960 pages, it’s a pretty good deal. I love the history in the first chapter, but haven’t found the rest of the book easy to use. It says it’s a reprint of a 1967 edition, but the prose feels older than that. It may be perfect for some students.I don’t see the reason for pointing out that Smith’s text is copyrighted. Any text is copyrighted automatically, regardless of whether or not the author puts a copyright notice on it. (The exception would be if the author explicitly places it in the public domain.) Unless a license to redistribute/repost the content is provided (think Creative Commons), what he tells people not to do is automatically prohibited by copyright law. Most likely he had someone try putting a copy of the text on their site, and he had a big battle to get it taken down, so he’s put that text on there.

Dale Hoffman of Bellevue College (east of Seattle) has written a calculus text that is now part of the Washington State Open Course Library Project: http://scidiv.bellevuecollege.edu/dh/Calculus_all/Calculus_all.html