Calculus Syllabus

Tier 5 Calculus Syllabus

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