Explanations
Calculus I
Explanatory essays must be typed, double-spaced, and handed in on a
separate page. Essays should be a page or two.
Explanations are graded on a ten-point scale in three
categories, with the first category counting for 50% of the grade, and the
latter two categories counting for 25% each. The categories are
- The explanation is mathematically correct and precise. The explanation
gives appropriate emphasis to the subtleties involved in the argument.
- The mechanics of the writing are correct; this includes things like
grammar, punctuation, spelling, paragraph structure, appropriate format,
and so on.
- The explanation is written in your own voice. The
explanation should show that you understand the ideas well enough that you
could explain them orally to me or a friend without referring to notes.
All explanations will cover topics that we have discussed in class.
Here's an
example of an essay that I wrote, explaining the
quadratic formula.
Assignments
September 2: Explain the derivation of the Law of Cosines
September 9: Explain the ε-δ definition of the limit.
September 23: Explain why the derivative of sin(x) is cos(x).
October 7: Explain why Fermat's Theorem holds.
November 4: Explain the definition of the Definite Integral.
November 18: Explain why the shell method works.
December 2: Explain why the derivative of ex is ex.
December 12: Discuss hyperbolic trigonometric functions.