I mentioned that several philosophers objected to calculus at
around the time of its development. In the 18th century, philosopher
published this rant
against calculus called
The Analyst: A DISCOURSE addressed to an infidel mathematician.
had loudly argued about some of the earliest formulations of calculus,
but his objections are clouded by a personal feud with mathematician
Extra Credit Assignment (due Monday May 1): turn in a one-page
summary of what Berkeley was complaining about (in your own words).
Did he have a point?
The Infinite Hotel is a story used to explain some ways that
"infinity" is different from "a really big number," for instance because
we would be justified in writing
and so on, but no big number satisfies these equations!
You can read about the Infinite Hotel
here and here.
of the definition of derivative at work.
(The closer and closer the red point gets to the green point, the better
and better the turquoise line starts to approximate the curve near the
Here are the three versions of Midterm 2:
If you submit solutions by Monday, May 15
to a version other than the exam you took in
class, it counts for extra credit.
applet. It's kind of complicated to figure out, but worth it.
You can tell it what function to plot, and you can slide around
the "hot point" and see how the derivative is changing.
Here is a related
rates handout from a calculus course at the University of British
Columbia. It has some great problems.
Extra credit assignment (due Monday, June 5): turn in as many of
these as you want (besides 7.9, which already appeared on homework).
Note: since many of these problems have the "short answer" included,
you will have to show detailed work to get credit.