AP Calculus AB

1: Limits and Continuity

• Understanding limits intuitively and graphically
• Computing limits analytically
• One-sided limits and limits at infinity
• Continuity and Intermediate Value Theorem

2: Derivatives

• Definition of the derivative as a limit
• Derivative rules (power, product, quotient, chain)
• Implicit differentiation
• Derivatives of trigonometric, exponential, and logarithmic functions

3: Applications of Derivatives

• Motion problems: velocity and acceleration
• Related rates
• Optimization problems
• Curve sketching: critical points, concavity, inflection points

 Integrals

• Antiderivatives and indefinite integrals
• Definite integrals and area under a curve
• Fundamental Theorem of Calculus
• Substitution method for integration

Applications of Integrals

• Area between curves
• Volume of solids of revolution (disk and washer methods)
• Accumulated change problems