Download Calculus I (Lamar University, 2007, 576 pages, 3,71 MB pdf file)

This notes not only contain the standard Calculus I material, but also (on the first 80 pages) a review of some precalculus topics. Dawkins has also written a nice Calculus Cheat Sheet and Calculus II and Calculus III notes.

Dawkins offers very good and thorough explanations. You will probably be able to understand them even if you have never heard about calculus before (if you already know a bit about calculus and want a quick refresher, the notes might be too verbose). There are many, many examples, the solutions are very carefully explained, not leaving out any intermediate steps. The notes also contain proofs, but these have been moved to the end of the notes.

After a review of some precalculus material ("only those topics that most students are particularly deficient in") Dawkins discusses limits, derivatives, applications of derivatives (including, among many others, optimization, linear approximations and Newtons method), integrals and applications of integrals (areas, volumes and the definition of work in Physics). The "Extras" chapter mostly contains the proofs.

You may also be interested in some other recommendations for Introductions to Calculus. And if you like Dawkins explanations, you might want to look at his other writings too, like his Notes on Complex Numbers.

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