The Calculus sequence is designed to be understood by every high schooler. This course can be used to prepare students for the AP BC Calculus examination.
Students will learn the ancient origins of the infinitesimal and they will see how such an idea can have a profound impact on the understanding of the world around us.
Students will be amazed at how calculus helps explain phenomena involving movement, population growth, financial markets, capital investment value, atmospheric temperature and pressure, planetary motion, and electromagnetic radiation velocity.
To many American high school students, calculus is a set of tools and rules that do nothing, leaving the student to never comprehend the innate beauty and powerful practicality that is calculus.
In this sequence, we set out to recapture the intuitive essence of the mathematics presented to us by Newton and Liebniz.
This is the opening round of what will amaze students. The idea of the infinitesimal was borne from ancient times, and students will explore its roots and development over a period of 2000 years. Students will apply this concept to solve a range of practical mathematical problems involving areas and volumes.
topics include: xenon's paradoxes, derivation of pi, squaring curves, method of exhaustion, Cavalieri method, Wallis method, Fermat method, center of mass, volume of solids, limits, Riemann sums
The Fundamental Theorem™
In this chapter, students discover the ideas of incremental change, the derivative, and they discover that there exists a beautiful relationship between the integral and derivative. We call it... The Fundamental Theorem of Calculus.
topics include: instantaneous velocity, limits, infinitesimal change, derivative definition, application of derivative, optimization, least path, linear regression, fundamental theorem of calculus, series
The Science of Fluxions™
Isaac Newton was the first scientist/mathematician to codify the ideas of the calculus. He used it solve a range of amazing physical problems, and with it he was able to show unknown mathematical relationships present in the very laws of the universe. Students will spend their time making these same discoveries.
topics include: Kepler's Laws, Newton's Laws, optimization, power series expansions of functions, Gauss' Law, chain rule, L'Hopital's rule, local extremums, Newton's method, Euler's method, indefinite integrals, growth and decay problems
The Calculus sequence consists of three 30-hour workshops for a total of 90 hours of in-class material. Academic year sequences are held in 10 week classes each 3 hours long. Summer camps are held in a single week and cover 30 hours of material.
Classes consist of hands-on activities, practice problems, and concept synthesis. Academic year students are required to complete a minimal amount of practice problems.