I've been teaching college-level math for over 25 years. In 2015 I started recording screencasts of my lectures. The result is Calculus 3D, a channel with videos from a traditional Calculus 3 course. I hope you find them helpful as you advance in your study of mathematics.

Currently, I'm working on splitting up the longer full-lecture videos into shorter ones with more graphics and explanatory callouts. These shorter videos are designated by chapter/section/video number. So, Video 16.2.1 is short for chapter 16/section 2/video number 1. The chapter and section numbering more-or-less follows Stewart's text. The homework playlists have video solutions to the problems linked to below.

Video 14.8.5: Example of Lagrange Multipliers with Two Constraints
16:26
Video 14.8.5: Example of Lagrange Multipliers with Two Constraints
Video 14.8.4: Lagrange Multipliers with Two Constraints
7:52
Video 14.8.4: Lagrange Multipliers with Two Constraints
Practice Test Problem Number 4
7:53
Practice Test Problem Number 4
Proof the Nul(A) is a Subspace
10:23
Proof the Nul(A) is a Subspace
Example: Gaussian Elimination
7:48
Example: Gaussian Elimination
Video 14.8.3: Finding Extrema Using Lagrange Multipliers (Exampe 2)
16:40
Video 14.8.3: Finding Extrema Using Lagrange Multipliers (Exampe 2)
Video 14.8.2: Finding Extrema Using Lagrange Multipliers (Exampe 1)
18:09
Video 14.8.2: Finding Extrema Using Lagrange Multipliers (Exampe 1)
Video 14.8.1: Introduction to Lagrange Multipliers
11:14
Video 14.8.1: Introduction to Lagrange Multipliers
Video 16.8.4: More Notes on Stokes' Theorem
8:42
Video 16.8.4: More Notes on Stokes' Theorem
Video 16.5 Addendum: A Point-Wise Interpretation of Curl
14:06
Video 16.5 Addendum: A Point-Wise Interpretation of Curl
Video 16.8.3: Notes on Stokes'
8:37
Video 16.8.3: Notes on Stokes'
Video 16.8.2: Using Stokes' Theorem to Evaluate a Line Integral
19:46
Video 16.8.2: Using Stokes' Theorem to Evaluate a Line Integral
Video 16.8.1: Introduction to Stokes' Theorem
6:37
Video 16.8.1: Introduction to Stokes' Theorem
16.6.3B: Parameterizing the Lower Half of an Ellipsoid
3:38
16.6.3B: Parameterizing the Lower Half of an Ellipsoid
Video 16.4.6: Conservative Vector Fields, Path Independence, and Line Integrals on Closed Curves
9:37
Video 16.4.6: Conservative Vector Fields, Path Independence, and Line Integrals on Closed Curves
Video 16.4.7: Green's Theorem Ties Up a Loose End
2:03
Video 16.4.7: Green's Theorem Ties Up a Loose End
Video 16.4.5: Using a Line Integral of Compute the Area of a Region
8:17
Video 16.4.5: Using a Line Integral of Compute the Area of a Region
Video 16.4.4: Green's Theorem Extended to a Region with a Hole
11:58
Video 16.4.4: Green's Theorem Extended to a Region with a Hole
Video 16.4.3: Green's Theorem on a Heart-Shaped Region
12:26
Video 16.4.3: Green's Theorem on a Heart-Shaped Region
Video 16.4.2: Partial Proof of Green's Theorem
14:46
Video 16.4.2: Partial Proof of Green's Theorem
Video 16.4.1: Green's Theorem with a Quick Example
7:40
Video 16.4.1: Green's Theorem with a Quick Example
Video 16.1.1: Introduction to Vector Fields (Redux)
9:58
Video 16.1.1: Introduction to Vector Fields (Redux)
Video 16.3.4: Recovering a Potential Function from F(x,y)
9:16
Video 16.3.4: Recovering a Potential Function from F(x,y)
Video 16.3.3: Showing a 2D Vector Field is Conservative
5:52
Video 16.3.3: Showing a 2D Vector Field is Conservative
Video 16.3.2: Evaluating a Line Integral using the Fundamental Theorem of Line Integrals
3:06
Video 16.3.2: Evaluating a Line Integral using the Fundamental Theorem of Line Integrals
Video 16.3.1: The Fundamental Theorem of Line Integrals
10:52
Video 16.3.1: The Fundamental Theorem of Line Integrals
Video 16.2.8: The Sign of a Line Integral Over a Vector Field From Its Graph
7:44
Video 16.2.8: The Sign of a Line Integral Over a Vector Field From Its Graph
Video 16.2.7: Evaluating a Line Integral in Differential Form
11:25
Video 16.2.7: Evaluating a Line Integral in Differential Form
Video 16.2.6: Differential Form of a Line Integral
4:25
Video 16.2.6: Differential Form of a Line Integral
Video 16.2.5: Computing a Line Integral W.R.T. a Vector Field
8:00
Video 16.2.5: Computing a Line Integral W.R.T. a Vector Field