1000.1 Lowering the Water Table
Recently a student asked me about a hydrology problem where drilling a well posed a threat to a nearby wetland.
A simplified version of this problem would make a good project.
We checked some references and I could see how to simplify the geometry for the aquifer so we could see some basic results.
There wasn't time to finish that work before this went to e-press.
In math there are many books with titles like "Analysis of Applied Mathematical Models" to give you ideas, for example, Mathematics for Dynamic Modeling by Edward Beltrami, Academic Press, 1987.
"UMAP Modules" should also be available in your math library.
These are similar to our projects - designed to show how undergraduate math is applied in a host of areas.
The specific topics used in the modules are specified at the beginning of each module.
The book Applications of Calculus, Philip Straffin, editor, MAA Notes Number 29, Mathematical Association of America, 1993, has more projects.
The robot arm looks like a good one.
The book Student Research Projects in Calculus by Cohen, Gaughan, Knoebel, Kurtz, and Pengelley, Mathematical Association of America, 1991, has still more.
Finally, I hope to expand and maintain a website for student projects in calculus.
1000.2 The Light Speed Lighthouse
For example, the lighthouse problem of Example CD 7.11 in the main text predicts that a beam of light will sweep down a straight shoreline faster than the speed of light.
Of course, this isn't so, but the part of the shore where it matters is far out.
The speed of the beam along the beach (in miles per second) is given by
But since c=186,000 miles per second, when D is a modest distance, the textbook answer is close, since
is small and the second formula gives the approximate speed
. When D tends to infinity, however, the limiting speed is c, as we see from the last formula.
The computations are easiest to illustrate with the computer and we will put a program on the website as soon as possible.
1000.3 Horizontal, Vertical, and Slant Asymptotes
Another traditional topic that is pretty dry on paper and much more fun with a computer is the study of horizontal, vertical, and slant asymptotes to graphs.
Again, look for a program on Asymptotes. Stay tuned.
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