AP Calculus

AP Calculus' Syllabus is set by the AP College Board, and
it includes the following:

Functions, Graphs, and Limits

  • Analysis of Graphs

  • Limits of Functions (1 and 2 sided limits)

  • Asymoptotic & Unbounded Behavior

  • Continuity

Differential Calculus

  • Concept of Derivative

  • Derivative at a Point & as a Function

  • Rules of Differentiation

  • Second Derivtives

  • Applications of Derivatives

    1. Equations of Tangent Lines

    2. Newtons Method

    3. Local Liear Approximations

    4. Curve Sketching

    5. Optimization Questions

    6. Instantaneous Rates of Change

    7. Motion

    8. Implicit Differentiation

Integral Calculus

  • Techniques of Antidifferentiation

  • First and Second Fundamental Theorms

  • Riemann Summs

  • Applications of Integration

    1. Areas Under Curves

    2. Volumes of Revolution

    3. Motion

    4. Solving Separate Differential Equations

    5. Exponential Growth Problems