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Polytechnic School's Mathematical Modeling II with Calculus BC

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

             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

             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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