Calculus—sometimes referred to as the mathematics of motion—was invented in the 17-th by the independent efforts of Isaac Newton and Goettfried Leibniz. However, many believe that were he able to accept the rather subtle notion of a limit, Archimedes would have actually invented the calculus millennia before the heyday of Newton and Leibniz.
Anyway, setting history aside, we shall be embarking on our first journey into analysis, the branch of mathematics containing calculus. (I recognize geometry and algebra as being the other two pillars of mathematics.) Your success will be the result of good preparation in both algebra and geometry, together with good old-fashioned hard work!
This marks the first year in which we have a dedicated level BC course in AP Calculus. We'll continue to use the same text as in years past, namely, CALCULUS, Graphical, Numerical, Algebraic, by Ross L. Finney, Franklin D. Demana, Bert K. Waits, and Daniel Kennedy, Scott Foresman Addison Wesley, New York, 1999, ISBN 0-201-32445-8, as this provides a decent exposure to the topics in both AB– and BC–level calculus. We'll pretty much follow the sequence suggested in the above text for the first seven chapters, except that I will regard the material in Chapters 1 (review of functions and trigonometry) and 2 (limits) review and will only touch lightly on these subjects. I will integrate the material of Chapter 8 into some of the discussions of the other chapters, and therefore there will not be a separate unit test over this chapter.
Our in-class unit tests will largely resemble the format of the externally-moderated AP Calculus examination (given in May) inasmuch as roughly half of the test will be multiple-choice format, with the remaining half being of free-response format.
A final comment is in order. Namely, there are a few points in the syllabus notes where I have ventured off on a some probability and statistics-related tangents. These notes should be of particular interest to students already having exposure to these topics (say, in our AP Statistics course). By bringing of this into the foreground, I hope to give such students a better understanding of both statistics as well as providing some meaningful applications of calculus. However, these topics are not essential for the understanding of this course.
Best wishes for a successful school year—Mr. "S."
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