# 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