3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Divergence, curl, and their relation to fluid flow and electromagnetism
3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Intuitions for divergence and curl, and where they come up in physics.
3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Divergence, curl, and their relation to fluid flow and electromagnetism
Khan Academy
Khan Academy: Multivariable Calculus: Gradient of a Scalar Field
Video finding a gradient in three dimensions by using an example about temperature in a 3-D room. Graph of the vector field found in the solution is shown. [10:54]
Khan Academy
Khan Academy: Multivariable Calculus: Gradient 1
Video lesson introducing gradients in two dimensions by calculating a gradient and then explaining what it is using a 3-D graph. [9:45]
Khan Academy
Khan Academy: Calculus: Partial Derivatives of Vector Valued Functions
Video showing how to take the partial derivatives of a generalized vector-valued function by taking the partial derivative of each part of the function. Video is meant as a build-up to the videos on surface integrals. [10:07]
Khan Academy
Khan Academy: Calculus: Derivative of a Position Vector Valued Function
Video lesson defining the derivative of a position vector valued function by visualizing it and setting it up. [14:45]
Khan Academy
Khan Academy: Calculus: Differential of a Vector Valued Function
Video lesson reviewing position vector valued functions and their derivatives. Explanation does not contain any specific examples. [5:04]
Khan Academy
Khan Academy: Calculus: Conceptual Understanding of Flux in Three Dimensions
Video explaining flux through a two-dimensional surface by relating it to line integrals in two dimensions. Sets up a surface integral of the dot product of the product of a mass density function and velocity function with the unit...
Khan Academy
Khan Academy: Calculus: Vector Representation of a Surface Integral
Video using the information about unit normal vectors to represent the surface integral for finding flux through a surface in two dimensions in a different way. The video also uses partial derivatives and the second definition of the...
Khan Academy
Khan Academy: Calculus: Vector Valued Function Derivative Example
Video lesson solving for the derivatives for a two specific vector-valued functions that describe the same path but have different velocities. [12:45]
Crash Course
Crash Course Physics #3: Integrals
This Crash Course Physics episode explains the ways that integrals can help us figure out things like distance when we have several other key bits of information. [10:08]
Khan Academy
Khan Academy: Multivariable Calculus: Position Vector Valued Functions
Video lesson explaining position vector-valued functions by visualizing and setting one up. [7:45]
Khan Academy
Khan Academy: Derivative of a Position Vector Valued Function
Video lesson defining the derivative of a position vector valued function by visualizing it and setting it up.
Khan Academy
Khan Academy: Differential of a Vector Valued Function
Video lesson reviewing position vector valued functions and their derivatives.
Khan Academy
Khan Academy: Green's Theorem: Green's Theorem Proof Part 1
Part 1 of the proof of Green's Theorem
Khan Academy
Khan Academy: Green's Theorem: Green's Theorem Proof (Part 2)
Watch a video to explore part 2 of Green's Theorem.
Khan Academy
Khan Academy: Green's Theorem: Green's Theorem Example 2
Watch a video for Green's theorem.
Khan Academy
Khan Academy: Vector Valued Function Derivative Example
This video has concrete example of the derivative of a vector valued function to better understand what it means.
Khan Academy
Khan Academy: Proof of Stokes' Theorem: Stokes' Theorem Proof Part 6
This is part six of the series of videos about the Stoke's Theorem.
Khan Academy
Khan Academy: Types of Regions in Three Dimensions
Watch a short video clip tp review the definition of Type 1 regions and visualizing what is and isn't a Type I region.
Khan Academy
Khan Academy: Proof of Stokes' Theorem: Stokes' Theorem Proof Part 5
This is part five of a series of video about the Stoke's Theorem.
Khan Academy
Khan Academy: Stokes' Theorem: Stokes Example Part 4 Curl and Final Answer
Finding the curl of the vector field and then evaluating the double integral in the parameter domain
Khan Academy
Khan Academy: Types of Regions in Three Dimensions
Students watch a video tutorial to learn about the divergence theorem.