Although this is not an AP course, it is designed to prepare the students for the next appropriate step in their mathematical education by providing them with the mechanics needed to solve problems in the two fields of calculus, differentiation, and integration. It will begin with a brief review of important pre-calculus concepts followed by an introduction to limits and continuity. At this point the girls will begin to examine the age-old question; "What is calculus and why do we need it?" As they answer this query, the students will begin their study of calculus by using the definition of the derivative and the limiting process to derive the basic rules of differentiation that can be applied to any type of function or relation. Practical applications of problems involving related rates, velocity, acceleration, and minimum and maximum values, will enhance the girls' understanding of the critical role calculus plays in fields such as engineering, architecture, rocket science, physics, economics, and others. The students will conclude their investigation of differential calculus with curve analysis and differentials. They will spend the final few weeks exploring the second important field of calculus, integration. At this point, they will begin to study antiderivatives and use integrals to find the area under a curve.
It has been said that one can never study too much calculus. Each time we revisit the topics of limits, derivatives, and integrals, their meaning becomes clearer. As a result, this course allows the college-bound seniors to feel comfortable in their college calculus course while preparing the remaining girls for AP Calculus.