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Calculus BC
The first thing you should understand
about Calculus BC is that the "B" in "BC" is the same as the "B" in "Calculus
AB." Therefore, if you have completed the Calculus AB syllabus, you have
already learned the "B" material. So in the MMII/BC course, you will review
that "B" material during the first semester, while you are learning about
fractals and chaos. The second semester will be devoted to the "C" material,
which will be new to you. This is reflected in the title of the textbook
for the second part of the course:
AP Calculus: The "C" Topics. It was written especially for MMII/BC
students at Polytechnic
School.
1.
Infinite Series
In
a break with tradition, we study the most difficult
of the "C" topics first. The subtilties and intricacies of
infinite
series require minds that are much fresher than
those
of most students at the end of their senior year.
2.
Antiderivatives and Integrals
We
review the Riemann sum concept and use it to set up
applications of various types. As a bonus, we give a "rigorous"
proof
of the Fundamental Theorem of Calculus. We study
antidifferentiation
by parts, by partial fractions, and by
substitution. Finally,
we give thorough attention to improper
integrals.
3.
The Calculus of Vector, Parametric, and Polar Functions
Our
theme is motion in the plane, even in the study of polar
coordinates
where we look at polar functions as "distance
modulators."
This idea, first suggested by Richard Sisley of
Polytechnic
School, replaces the more static traditional
approach
to polar functions with a more dynamic
interpretation.
4.
Differential Equations
We
extend the students' knowledge of the simple growth-decay
models
of the AB syllabus to the case of bounded growth. The
primary
model here is the logistic differential equation, which
was
added to the the BC syllabus in 1998. A unique feature of
the
MMII/BC class is that, during the first semester of the class,
students
make a thorough study of the logistic difference
equation
in the context of pioneering work in chaos and
bifurcation
theory by Robert May and Mitchel Feigenbaum .
This
allows for some very rich discussion about the interplay
between
discrete and continuous models of dynamical systems.
For a more detailed outline of the coverage of the "C"
topics, see the table of contents
for AP Calculus: The "C" Topics. Also, see the College Board's
official AP Calculus site for complete information about the BC syllabus.
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