Calculus Syllabus

Tier 5 Calculus Syllabus

Download the Calculus Syllabus PDF

Part 1.  Differential Calculus (14 Lessons)

  • T5 C1 Introduction to Calculus
    • Approach to Learning Calculus
    • Calculus Overview
  • T5 C2 Function; Graph Terms for Functions
    • Function Graph Terms Sheet for Calculus
    • Function Graphs #1 Worksheet
    • Examples of Graphs
  • T5 C2a Functions
    • More Examples
  • T5 C3 Derivative
    • Differential Calculus
    • Infinitesimals
    • Derivative definitions
    • Examples
  • T5 C4 Derivative Examples
    • From definition
    • From Wolfram Alpha
  • T5 C5 Applications to Graphing
    • Increasing/Decreasing
    • Max/Min
    • Points of Inflection
    • Concavity
  • T5 C6 Derivative Rules
    • Linear combination Rule
    • Leibniz Rule
    • Quotient Rule
  • T5 C7 Chain Rule
    • Derivative Examples from Rules
    • Wolfram Alpha examples
  • T5 C8 Implicit Differentiation
  • T5 C9 Relative Rates of Change
  • T5 C10a Inverse Functions Basics
  • T5 C10 Inverse Functions
  • T5 C11 Series Expansions
  • T5 C12 Final Thoughts on Derivatives

Part 2. Integral Calculus (18 Lessons)

  • T5 C13 Integral Calculus Overview
  • T5 C14 Definition of Integral and the FTC
  • T5 C15 Techniques of Integration Overview
  • T5 C16 Applications of Integration Areas
  • T5 C17 Applications of Integration Arc Length
  • T5 C18 Applications of Integration Volumes Disc
  • T5 C19 Applications of Integration Volumes Shell
  • T5 C20 Applications of Integration  Surface Areas
  • T5 C21 Parametric Functions Graphs
  • T5 C22 Parametric Functions Arc Length
  • T5 C23 Parametric Functions Tangent Line
  • T5 C24 Parametric Functions Area
  • T5 C25 Wolfram Alpha Commands
  • T5 C26 Improper Integrals Vertical Asymptotes
  • T5 C27 Improper Integrals Horizontal Asymptotes
  • T5 C28 Improper Integrals Horizontal Asymptotes continued
  • T5 C29 Surface areas of solids revisited
  • T5 C30 Wolfram Alpha Modern STEM Tool