Outline

# Calculus

## Table of Contents

### Preliminary Material

- Notice and Wonder (Red Circle)
- Notice and Wonder (function and triangle)
- Notice and wonder (rectangles and trapezoids)
- Notice and Wonder (points on a curve)
- Notice and Wonder (plane and shapes)
- Notice and Wonder (sectors)
- Notice and Wonder (Sam's Circle)
- Particle Moving Along a Line
- Copy of Method of Exhaustion

### Limits

- Notice and Wonder (piecewise-defined function)
- Limits of Piecewise-Defined Function #1
- Limits of Piecewise-Defined Function #2
- Limits of Piecewise-Defined Function #3
- Visualizing the definition of a limit 1
- Visualizing the definition of a limit #2
- Epsilon-delta definition of a limit
- The Squeeze Theorem (I): Clearly Illustrated???
- Squeeze Theorem
- Squeeze Theorem Example
- Limits

### Derivatives

- Particle Moving Along a Line--Velocity and Displacement
- Investigating Secant Lines
- Intuitive Derivative Graphing Exercise: REVAMPED!!!
- Position, Velocity, and Acceleration vs. Time Graphs
- derivative of inverse functions
- Average Rate of Change
- Derivative of the Area of an Equilateral Triangle
- Piecewise Functions: Continuity & Differentiability

### Integrals

- Riemann Sums
- Volume of a watermelon
- Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions
- Solids Formed From Certain Cross Sections
- fundamental theorem of calculus
- Solids - Square cross sections
- Solids of Revolution - Shell method and estimations
- Solids - Isosceles right triangle cross-sections
- Area between curves with Riemann sums
- Solid of Revolution
- Solids of Revolution (Discs)
- Disc Action!!!
- Washer Method: REVAMPED!
- The Fundamental Theorem of Calculus
- Surface with Square Cross Sections

### Differential Equations

### Miscellaneous

### Theorems and Definitions