Mathematics

There is more to elementary calculus than may first meet the eye, even to those of us who have learned (or taught it) at various levels. With appropriate help from graphical, numerical, and algebraic computing, well-worn calculus techniques and topics---polynomials, optimization, root-finding, methods of integration, and more---often point to deeper, more general, more interesting, and sometimes surprising mathematical ideas and techniques. I'll illustrate my thesis with figures, examples, and a lot of e-calculation, aiming to take elementary calculus to its interesting extremes.