An advanced placement course in differential and integral calculus. Topics: functions and graphs, a rigorous development limits, continuity, derivatives and differentiability, applications of the derivative, curve sketching, related rates, implicit differentiation, parametric equations, polar functions, vector functions, l’Hospital’s rule, Riemann sums, indefinite and definite integrals, techniques of integration, applications of integration, the Fundamental Theorem of Calculus, numerical approximations to definite integrals, improper integrals, differential equations, polynomial approximations, Taylor series, limit comparison test, alternating series error bound and absolute and conditional convergence and divergence of infinite sequences and series. This course prepares students for the AP Calculus BC exam.
AP Calculus BC
Honors Precalculus with Trigonometry (OM013)