AP Calculus AB - Topics
 Topics Pre Calculus Review Prerequisites for Calculus: Precalculus Review Average rate of change Elementary functions and graphs Function arithmetic and composition Limits Concept of limit Finding limit graphically and numerically Properties of limits Intermediate theorem Squeeze theorem Introduction to Derivative Concepts and types of continuity and discontinuity Average and instantaneous rate of change Definition of derivative Computing derivative function from the definition Local linearity Derivative at a given point Secant and tangent line at a given point Derivative as a rate of change Estimating the average and instantaneous rate of change from data and it graphs Motion, position, velocity and acceleration functions Differentiability and continuity Power rule Product rule Quotient rule Chain rule Special Functions Trigonometric function, exponential functions, and logarithmic functions Graphs of trigonometric function, exponential functions, and logarithmic functions Derivatives of trigonometric Functions, exponential functions, and logarithmic functions Derivative of ln x and ex Implicit Differentiation and Calculus of Inverse Function Finding derivative implicitly Differentiation notation Inverse functions: exponential and logarithmic functions Calculus of Inverse functions Inverse trigonometric functions Calculus of Inverse trigonometric functions Calculus of Hyperbolic functions Comparing graphs of f and f ' Practical Application of the Derivative Position, velocity, and acceleration Critical points Finding extrema and increasing and decreasing behavior of a curve Local and absolute extreme values Higher derivative and linear approximation Newton’s method Related rates Optimization   Curve Sketching Finding critical points, local minimum and maximum on a curve Comparing the graphs of f , f ' and f '' The first and second derivative tests Concavity and inflection points Estimating derivative from data and graphs Asymptotes and infinite limits Intermediate value theorem Mean value theorem Rolle’s theorem The Basics of Integration Antidifferentiation Antiderivatives of Powers of x Antiderivatives of Trigonometric and Exponential Functions Undoing the Chain Rule Integrating Polynomials by Substitution Integrating Composite Trigonometric Functions by Substitution Integrating Composite Exponential and Rational Functions by Substitution More Integrating Trigonometric Functions by Substitution Choosing Effective Function Decompositions Approximating Areas of Plane Regions Areas, Riemann Sums, and Definite Integrals The Fundamental Theorem of Calculus, Part II Illustrating the Fundamental Theorem of Calculus Evaluating Definite Integrals An Introduction to the Integral Table Deriving the Trapezoidal Rule An Example of the Trapezoidal Rule   Applications of Integration Motion of a particle: net and total distance traveled Gravity and vertical motion Area bounded by curves Average value of a function Volume using cross-section Disk method Washer method Shell method Arch length Work and Hooke’s Law Moments and center of mass Separable differential equations Direction fields Growth and decay problems Logistic growth Exponential growth and radioactive decay