Since I'll be working ("I" being the original poster, Andrew L) as either a high school math teacher or adjunct at a university as well as private tutoring, to make ends meet for the next year or so (hopefully entering a PHD program after that, finally), I suspect I'll be teaching calculus a great deal and at several different levels. I wanted to ask what everyone's favorite calculus text is. What worries me about this question is the same problem the board seems to have whenever this kind of question is asked: Since many mathematicians begin as gifted students, they have—to put it kindly—unrealistic expectations of what level textbook most students can handle. For example, when asked about undergraduate topology texts for beginners, more then a few posters put Robert Switzer and Peter May's books. And in the same thread, Hatcher was listed as an undergraduate text. I suppose that'd be reasonable at Harvard or in Germany, where students actually have a reasonable education coming in. Unfortunately, this is America and whether or not students can read who enter college isn't a foregone conclusion.
Another problem that this question has is a lot of mathematicians choose a purely theoretical calculus course devoid of physical applications. The applications of calculus are not only incredibly important in their own right, but without them, a lot of the concepts of calculus become downright mysterious in not only their relevance, but how anyone ever thought of them. As beautiful as Michael Spivak's Calculus is—and it is quite wonderful—the fact that it only has one toy example involving celestial mechanics to me is a serious defect that would force me to supplement it extensively.
Here are my choices: For an honors course consisting of the very best students, I would use either Spivak supplemented with an extensive set of composed notes focusing on history and applications or the very unusual and wonderful book, Practical Analysis in One Variable by Donald Estep. Estep's book is clearly a calculus text which is being sold as an analysis text-this is what Estep thinks a general calculus course SHOULD look like. The book uses a rigorous approach to calculus through numerical approximation of physical models such as Verhulst population models, chemical equilibrium, Newtonian and Einsteinian mechanics and a lot more. It's a fascinating read and I highly recommend it to all.
For "regular" students, the choice is clear: Gilbert Strang's Calculus. Beautifully written, clearly motivated with lots of examples, applications and diagrams and nothing is thrown out without clear explanation. It's also more advanced then the usual plug-and-chug books in its choice of topics and applications—very careful without being rigorous. And lots of good conceptual exercises that will force students to think,rather then calculate mindlessly.
Ok, that's my 2 picks. What about everyone else? What calculus books would you use—and make clear what kinds of students you have. It matters!
