Calculus Course Outline

This course is designed to introduce students to Calculus. It also covers material compatible with the Calculus AB exam, enabling students to take the AB exam at the end of the year in preparation for college and college credits. This course uses Calculus: Early Transcendentals by Briggs & Cochran.

Semester I

Chapter 1: Functions

  • review of algebra topics as time allows
  • functions
  • inverses, exponentials, and logarithmic functions

Chapter 2: Limits

  • limits
  • infinite limits
  • continuity
  • limits at infinity

Chapter 3: Derivatives

  • rules of differentiation
  • product and quotient rules
  • differentiation of trig functions
  • the Chain Rule
  • implicit differentiation
  • derivatives of logarithmic and exponential functions
  • related rates

Chapter 4: Applications of the Derivative

  • maxima and minima
  • graphing functions
  • optimization problems

Semester II

Chapter 4: Applications of the Derivative

  • linear approximation and differentials
  • Mean Value theorem
  • L’Hopitals Rule
  • antiderivatives

Chapter 5: Integration

  • area under curves
  • definite integrals
  • the Fundamental Theorem of Calculus
  • working with integrals
  • substitution rule

Chapter 6: Application of Integration

  • velocity and net change
  • regions between curves
  • volumes by slicing
  • volume by shelss

AP Calculus Prep

  • review and preparation for Calculus AB exam

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