Professor Dave Explains
Stokes's Theorem
Stokes's Theorem is kind of like Green's Theorem, whereby we can evaluate some multiple integral rather than a tricky line integral. This works for some surface integrals too. Let's see how it works!
Professor Dave Explains
Gauss’s Law for the Electric Field
Maxwell's equations are the simplest way to represent the relationship between the electromagnetic field and it's carrier particle, the photon. Simple does not necessarily mean easy though. Let's dig into what Maxwell's formulas are and...
Professor Dave Explains
Faraday’s Law
A couple hundred years ago, Michael Faraday discovered that a changing magnetic field produces an electric field. What is the relationship between these two fields and how can we calculate it? Faraday's law deals with any open or closed...
Professor Dave Explains
The Divergence Theorem
Green's Theorem gave us a way to calculate a line integral around a closed curve. Similarly, we have a way to calculate a surface integral for a closed surface. That's the Divergence Theorem. This is also known as Gauss's Theorem, and...
Khan Academy
Khan Academy: Calculus: Example of Calculating a Surface Integral Part 1
Part 1 of a 3-part video series showing how to calculate the surface integral of a torus. Video first reviews the parametrization of the torus and then starts to use it to find the surface area of the torus by finding partial...
Khan Academy
Khan Academy: Calculus: Introduction to the Surface Integral
Video introducing surface integrals by building on the partial derivatives of vector-valued functions from the previous video and showing how to visualize a surface integral. Surface area is found by taking the magnitude of the cross...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt4: Home Stretch
Part 4 of a 4-part video series solving for the surface integral of a surface made of three separate parts. This video finishes evaluating the surface integral of the third surface and adds the results together. [4:02]
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt1: Parameterize the Outer Surface
Part 1 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The first video sets up the surface integral for the entire surface, evaluates the first surface and parametrizes and finds the...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex2 Pt2: Evaluating Integral
Second part of a two-part video series on calculating the surface integral of a surface that can be described as a function of x and y. Video evaluates the surface integral. [9:51]
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: Example of Calculating a Surface Integral Part 2
Part 2 of a 3-part video series showing how to calculate the surface integral of a torus. Video continues to find the surface area of the torus by calculating a cross product. [10:29]
Khan Academy
Khan Academy: Calculus: Example of Calculating a Surface Integral Part 3
This is part 3 of a 3-part video series showing how to calculate the surface integral of a torus.
Khan Academy
Khan Academy: Calculus: Surface Integral Ex1 Pt2: Calculate Surface Differential
Part 2 of a 3-part video series showing how to calculate the surface integral of the unit sphere.. Video calculates the cross product of the two vectors and its magnitude. [12:50]
Khan Academy
Khan Academy: Calculus: Surface Integral Ex1 Pt3: The Home Stretch
Part 3 of a 3-part video series showing how to calculate the surface integral of the unit sphere. Video calculates the double integral of the magnitude of the cross product found in the previous part. Trigonometric identities and...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt3: Top Surface
Part 3 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The third video parametrizes the third surface, finds the magnitude of the cross product and begins to evaluate the double...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt2: Evaluating the Outside Surface
Part 2 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The second video finishes evaluating the surface integral of the second surface by substituting a trigonometric identity. [9:10]
Khan Academy
Khan Academy: Divergence Theorem Proof: Divergence Theorem Proof (Part 2)
This is part two of the series of videos about the Divergency Theorem.