## 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.

The "C" Topics

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.