Vector Valued Function
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 Parameterization
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
Calculate 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
Tangential & Normal Components Of 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
Chapter Test
1 hr 39 min 15 Examples
- Determine whether the statement is true or false (Problems #1-5)
- When is the speed a minimum? (Problem #6)
- Find the length of the curve (Problem #7)
- Find parametric equations (Problem #8)
- Calculate the limit of the vector-valued function (Problem #9)
- Find the curvature (Problem #10)
- Reparameterize the curve (Problem #11)
- Find the velocity and position given the acceleration and initial velocity and position (Problem #12)
- Find the velocity, acceleration and speed of the particle (Problem #13)
- Calculate the tangential and normal components of the acceleration vector (Problem #14)
- Find the unit tangent, unit normal, and binormal vectors (Problem #15)
