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    2018 EXAM DATE: Tuesday, MAY 15th, morning session

    Topic Outline for Calculus BC

     

    The topic outline for Calculus BC includes all Calculus AB topics plus the additional topics below.

     

     

    1. Parametric, polar, and vector functions

    • Analysis of planar curves includes those given in parametric form, polar form, and vector form.

    • Derivatives of parametric, polar, and vector functions

    • Finding the area of a region (bounded by polar curves)

    • Finding the length of a curve (given in parametric form)

       

    1. Applications of derivatives

    • Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration

    • Numerical solution of differential equations using Euler’s method

    • L’Hôpital’s Rule, including its use in determining limits and convergence of improper integrals and series

     

    1. Applications of integrals

    • Finding the length of a curve

    • Antiderivatives by substitution of variables (including change of limits for definite integrals), parts, and simple partial fractions (nonrepeating linear factors only)

    • Improper integrals (as limits of definite integrals)

    • Solving logistic differential equations and using them in modeling

     

    1. Polynomial Approximations and Series

       

    • Concept of series A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence.

    • Series of constants

      • Motivating examples including decimal expansion

      • Geometric series with applications

      • The harmonic series

      • Alternating series with error bound

      • Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series

      • The ratio test for convergence and divergence

      • Comparing series to test for convergence or divergence

    • Taylor series

      • Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve)

      • Maclaurin series and the general Taylor series centered at x = a

      • Maclaurin series for the functions ex, sin x, cos x, and

      • Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series

      • Functions defined by power series

      • Radius and interval of convergence of power series

      • Lagrange error bound for Taylor polynomials