**Vector Functions**

## Vector Functions and Space Curves

44 min 7 Examples

- 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

42 min 6 Examples

- 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

38 min 4 Examples

- Overview Arc Length
- Example #1 finding Arc Length of a 3-D Vector Function
- Example #2 finding Arc Length of a 3-D Vector Function
- Overview Reparameterization
- Example #1 Reparameterizing a Curve with Respect to Arc Length
- Example #2 Reparameterizing a Curve with Respect to Arc Length

## Curvature

24 min 3 Examples

- 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

23 min 4 Examples

- 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

14 min 2 Examples

- 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