Incomplete Specs for Project 4, draft of 6 November 2000.
Please follow any revisions on our website.
"A Compact Example from the Early Calculus"
This project may be done in groups. The group need not be your traditional
on, it may be reconstituted along common interests. It is to be a "report",
but may have the format of a "lesson plan" (your peers are the audience),
an "essay", a "public presentation", etc.
Here are a few ideas for you to consider and do some preliminary research on.
1. The Simple Pendulum.
2. The Brachistochrone Problem. (Huygens)
3. The Cycloid, the Helen of Geometry.
4. Napier's Logarithms. (See Edwards ... summarize or extract.)
5. Contrast and compare the treatment of one topic from the elementary calculus
in a textbook 1850-1900, 1900-1950, 1950-1990, 1999-2000, in C&M, on Web??
(a) The Chain Rule
(b) Integration by Partial Fractions.
(c) Newton's part of the FTC (Mean Value Theorems)
(d) .... you choice...
6. Applications of the Binomial Theorem to the Calculus (see Edwards)
7. Conic Sections: derive (1/r) = p + e cos(theta) from the definition,
namely a plane cutting a cone.
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