AP Calculus

AP Calculus, or Advanced Placement Calculus, refers to the two Advanced Placement Calculus courses run by the College Board. The two courses are AP Calculus AB and AP Calculus BC. AP Calculus AB is supposed to be roughly equal to the first semester and a half of a typical year-long introductory, single-variable college calculus course, while AP Calculus BC is allegedly equal to the full year. Students may take the AP Calculus AB or BC exam administered every year in May for potential college credit. Like all other AP courses, students need not to actually take the class; they may take just the exam for possible college credit.

Course Content

The AP Calculus AB covers the following topics:

• Limits
  • Rational functions
  • Trigonometric, logarithmic, and exponential limits
  • Properties of limits
  • Limits at infinity
• Continuity
  • Showing a function is continuous at a point
• Differentiation
  • Definition of derivative
  • Linear differentiation rules
  • Product, quotient, and chain rule
  • Trigonometric, exponential, and logarithmic functions
  • Logarithmic differentiation
  • Second and higher order differentiation
• Applications of the derivative
  • Mean Value Theorem, Intermediate Value Theorem, and Extreme Value Theorem (MVT, IVT, EVT)
  • Optimization and Related Rates
  • Linear approximation
  • Concavity
  • Relationship to position, velocity, and acceleration
• Integration
  • Properties of integration
  • Fundamental Theorem of Calculus
  • Indefinite Integrals
    • substitution (reverse chain rule)
    • Partial fraction decomposition
    • Integration by parts
  • Improper Integrals
• First order differential equations
  • Modeling exponential growth/decay with differential equations
  • Separable differential equations
  • Euler's method
• Applications of the definite integral
  • Net change
  • Relationship to position, velocity, and acceleration
  • Areas in the plane
  • Volumes of cross sections
  • Solids of revolution