The Colorado School of Mines Calculus Worksheets
by
Jack K. Cohen

Objectives
At Colorado School of Mines, we are using Mathematica in all sections of first year calculus. We have opted to treat Mathematica as a gradually learned tool to supplement the course. Thus, we consciously restrict the statements learned to a small set. We have, of course, made some changes in the curriculum reflecting the existence of such tools and, certainly, we will make more such as we gain experience.

The initial changes are in such obvious areas as lowering emphasis on learning tricky integration techniques. The initial material we want to add is an increased emphasis on problem solving: mathematical modeling (``story problems''), frequent use of parameters in addition to strictly numeric examples, an increased emphasis on more realistic problems, in particular, on physical ones.

Usage
These worksheets (all have answer sheets) may be used for cooperative education teaching or simply as homework. In any case, I hope they include ideas about the use of Mathematica or other symbolic tools that will be practical for a wide spectrum of teaching techniques.

Other Materials
We will eventually also disseminate Mathematica Projects and classroom demonstation code.

Special Pleading
Please don't look at the very first worksheet and quit because that one doesn't excite you. I hope that if you look at 3 or 4 of them, you'll see where we are headed and be willing to come along with us at least part way. Also, it definitely not my intent to replace the text. Hence although I have no reference to such things as the extended discussion in our test concerning the slope of a parabola or the limit laws in the worksheets, be assured I do to cover such matters in a more conventional manner.

Acknowledgements
We use the Edwards and Penney text, Edition 3. The problem numbers in the worksheet refer to this text. For example, the reference (2.3.26) means problem 26 at the end of section 2.3 in E&P. In many cases—without noting it—I have altered the E&P problems somewhat to adapt them to my needs. In the early part of the course, I also build a number of problems around some material from the Teacher's preface section of E&P.

We are also looking at materials from the Calculus Reform movement such as the St. Olaf materials. I intend to cite these sources on my worksheets—if I slip, please don't hesitate to put me right.

Finally, I owe thanks to my teaching colleagues at Colorado School of Mines, Barbara Bath, Duane Haugen, Ingrid Fontino, and especially to Frank Hagin, my good friend for many years and the initiator of our Mathematica calculus project.