AP Calculus AB Course Outline

1. Limits and Continuity

• Definition of limits
• Evaluating limits graphically and algebraically
• Continuity of functions

2. Differentiation

• Derivative definition and basic rules
• Applications of derivatives
  • Rate of change, velocity, and related rates
• Higher-order derivatives

3. Integration

• Antiderivatives and indefinite integrals
• Definite integrals and the Fundamental Theorem of Calculus
• Applications of integrals
  • Area under a curve, volume of solids of revolution

4. Applications of Integration

• Techniques of integration
  • Substitution, integration by parts
• Applications to physics and economics

5. Differential Equations

• Slope fields and Euler's method
• Separation of variables and solving first-order differential equations

6. Polynomial Approximations and Series

• Taylor and Maclaurin series
• Convergence and divergence of series
• Power series and interval of convergence

7. Parametric Equations and Polar Coordinates

• Parametric equations and their derivatives
• Polar coordinates and graphs
• Conic sections in polar coordinates

8. Review and Exam Preparation

• Review of key concepts and topics
• Practice exams and questions
• Exam-taking strategies