## Vector Functions and Space Curves

- Overview of Vector-Valued Functions, Plane Curves, and Space Curves
- Example of finding a vector function
- Finding Limits of Vector Functions Overview
- Example #1 of finding Limits of Vector Functions and identifying its domain
- Example #2 of finding Limits of Vector Functions and identifying its domain
- Example #3 of finding Limits of Vector Functions and identifying its domain
- Example #4 of finding Limits of Vector Functions and identifying its domain
- Overview of Finding Continuity for Vector-Valued Functions with Two Examples
- Representing Space Curves: Helix
- Identifying a Space Curve Example

## Derivatives and Integrals of Vector Functions

- Overview of how to find to find Derivatives and Integrals of Vector Functions
- Finding the Tangent and Unit Tangent vector Example
- Example of finding Parametric Equations of the tangent line
- Example of finding the second derivative of a vector function
- Definition of a Smooth Curve with Two Examples
- Differentiation Rules for Vector Functions
- Integration Rules for vector Functions
- Two Examples of Integrating Vector Functions
- Example of how to write and integrate a vector function given an initial condition

## Arc Length and Reparameterization

- Overview of Arc Length for 2-D and 3-D Formulas
- Two Examples of Finding the Length of a Curve for a Vector-Valued Function
- Overview of Reparameterization
- Two Examples of Reparameterizing in terms of Arc Length

## Curvature

- Overview of Curvature and its Formulas
- Example of Finding Curvature using the Unit Tangent Vector
- Example of Finding Curvature using the cross product
- Example of Finding Curvature for a function

## Unit Tangent Vectors

- Overview of the Unit Tangent, Normal and Binormal Vectors
- Example of finding the tangent vector
- Finding the Unit Tangent Vector Example
- Finding the Unit Normal Vector Example
- Finding the Binormal Vector Example

## Motion in Space: Velocity and Acceleration

- Overview of the Tangential and Normal Components for Acceleration
- Example of finding the Tangential and Normal Components of Acceleration in 3D
- Example of finding the Tangential and Normal Components of Acceleration in 2D