AP Calculus

Big Idea 1: Limits
  • Limits in Calculus
    • Obj. 1: Limit Notation & Basic Definition
    • Obj. 2: Reviewing continuous functions. 
    • Obj. 3: Limits and Discontinuity 
    • Obj. 4: Estimating Limits Graphically
    • Obj. 5: Evaluating Limits Algebraically 
    • Obj. 6: Formal Definition of Continuity 
    • Obj. 7: One-Sided Limits
    • Obj. 8: Nonexistent Limits
    • Obj. 9: Limits & Infinity
    • Obj. 10: Intermediate Value Theorem, Extreme Value Theorem, Mean Value Theorem
  • L-Hospital's Rule for Indeterminate Forms (learn after reviewing Big Idea 2)

Big Idea 2: Derivatives

  • Definition of a Derivative and the Difference Quotient
  • Estimating the Derivative
  • Derivative Rules
  • Derivative Applications
  • Related Rates & Optimization 
  • The Chain Rule
  • Implicit Differentiation
  • Derivative of an Inverse Function
  • Vector-, Parametric-, and Polar Forms of Derivatives
  • Higher Order Derivatives
  • Differentiability and Continuity
  • Analyzing Functions using Derivatives
  • Analyzing Functions using Derivatives in Polar Form 

Big Idea 3: Integrals

Big Idea 4: Series (BC)

Extra:

  • Epsilon-Delta Definition of a Limit

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