All of the following came from Collegeboard's Course Discription of AP Calculus

Topic Outline for Calculus AB
I. Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (Including one-sided limits)
Asymptotic and unbounded behavior
Continuity as a property of functions
+ Parametric, polar, and vector functions. The analysis of planar curves includes those given in parametric form, polar form, and vector form.

II. Derivatives
Concept of the derivative
Derivative at a point
Derivative as a function
Second derivatives
Applications of derivatives
+ Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration vectors.
+ 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.
Computation of derivatives
+Derivatives of parametric, polar, and vector functions.

III. Integrals
Interpretations and properties of definite integrals
Applications of integrals
Fundamental Theorem of Calculus
Techniques of antidifferentiation
+ 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).
Applications of antidifferentiation
+ Solving logistic differential equations and using them in modeling.
Numerical approximations to difinite integrals

+IV. Polynomial Approximations and Series
Concept of a series

+ explaination of what a series is and when it converges (looking at the sequence of partial sums).
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 uses 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 function e^x, sinx, cosx, and 1/(1-x)
+ 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.