This course covers all the topics in the Advanced Placement BC Calculus syllabus and goes beyond. The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include vectors and vector-valued functions, parametric equations, polar functions and polar area, differentiation, integration and the Fundamental Theorem of Calculus, improper integrals, sequences and series, Taylor expansions with Lagrange Error Bound, logistic differential equations.

Topics covered beyond the BC syllabus include integral applications to physics and engineering, biology and economics – work, electricity, energy, hydrostatic force, moments, centers of mass, Poiseuille’s Law, cardiac output, consumer surplus, present and future value – surface area, probability, advanced techniques of integration, epsilon-delta definition of limit, curvature, modeling using differential equations, predator-prey systems and Fourier series. A TI-84 graphing calculator is required. Students are required to sit for the AP Exam. (1 credit) Prerequisite: Completion of AB Calculus: Placement by the Math Department