Beginning Fall 2009, I'm teaching Calculus to some of Stern's business majors, aiming to connect basic concepts to how they are applied in business and economics, while preserving a rigorous syllabus and continuing to emphasize the mathematical beauty of some of the basic theorems.
To me, learning calculus is like learning a new language, and imparts an elegant yet powerful way of expressing and understanding ideas both simple and complex. This page contains a selection of some links to articles, web sites and other forms of content that I've enjoyed or found useful when teaching, learning or thinking about calculus. Let me know if there are others I can add.
(this page is a constant work in progress,...)
My syllabus, circa September 8th, 2009
Textbooks I've considered
Calculus for Business, Economics, Life Sciences and Social Sciences, 11th Edition: This is the textbook I'm using in 2009. It does well on the applications, detailed explanations and illustrations, but lacks detail on the theory and proofs, so I'm having to supplement many of the basic theorems with notes of my own.
Essential Calculus: Early Transcendentals: This is a very popular textbook, used by our Math department (and about half the others I surveyed). It provides a concise treatment with good proofs and a terse style, but lacks sufficient range in its examples, especially from business and economics.
Differential and Integral Calculus by N. Piskunov. This is the textbook I used in high school and as a freshman in college. I recall it being a really, really good book with lots of examples and well-explained theory. Sadly, it is out of print, and owed it's 1980's international fame in part to being published by Mir Publishers and subsidized heavily for export by the Soviet Union.
Books/notes that can liven up the experience
I am not vouching for their mathematical content, but they may make you smile.
How to Ace Calculus: The Streetwise Guide
The Manga Guide to Calculus
The Derivative Comic
Calculus for Dummies
Finite Simple Group (of Order Two) (this requires a lot more than Calc 1 to understand fully, but has a nice tune even if you haven't had the other courses).
History of Calculus (wikipedia)
Scroll down for some more geeky calculus cartoons