Instructional Video15:05
Professor Dave Explains

Vector Fields, Divergence, and Curl

9th - Higher Ed
An introduction to vector fields.
Instructional Video12:23
Professor Dave Explains

Evaluating Line Integrals

9th - Higher Ed
An introduction to line integrals.
Instructional Video14:56
Virtually Passed

A better way to understand Differential Equations | Nonlinear Dynamics (Part 4) | Index Theory

Higher Ed
Index theory is a method used to gain global information about a nonlinear differential equation. One powerful insight is that closed orbits (periodic solutions) must have at least one fixed point inside of the curve....
Instructional Video
Khan Academy

Khan Academy: Calculus: Curl 2

9th - 10th
Video demonstrating how to calculate curl for a specific three-dimensional vector field. [10:17]
Instructional Video
Khan Academy

Khan Academy: Calculus: Divergence 1

9th - 10th
Video introducing divergence by calculating it for two specific vector fields. Begins to explain the intuition behind divergence by drawing a particular vector field. [10:20]
Instructional Video
Khan Academy

Khan Academy: Multivariable Calculus: Gradient of a Scalar Field

9th - 10th
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]
Instructional Video
Khan Academy

Khan Academy: Calculus: Divergence 2

9th - 10th
Video lesson continuing an introduction of divergence by using the graph of a particular vector field, calculating the divergence and explaining what it means for the example. Works through three more examples in the same way. Examples...
Instructional Video
Khan Academy

Khan Academy: Calculus: Divergence 3

9th - 10th
Video demonstrating how to find the divergence for a two-dimensional vector field, calculating when the divergence would be positive or negative, and analyzing the graph of the vector field. [10:48]
Instructional Video
Khan Academy

Khan Academy: Calculus: Curl 1

9th - 10th
Video lesson introducing curl by analyzing the graph of a vector field for an example of a twig moving along with the current. Relates curl to the del operator, divergence, and gradient. [9:32]
Instructional Video
Khan Academy

Khan Academy: Vector Field Line Integrals Dependent on Path Direction

9th - 10th
Video lesson using line integrals in a vector field for a path in opposite directions. Gives the intuition and then shows that the results will have opposite signs.
Instructional Video
Khan Academy

Khan Academy: Thanksgiving Math: Green Bean Matherole

9th - 10th
A Thanksgiving dinner compared to a vector field.
Instructional Video
Khan Academy

Khan Academy: Viewing G as Value of Earth's Gravitational Field Near the Surface

9th - 10th
Sal Khan explains g as the value of Earth's gravitational field near the surface rather than the acceleration due to gravity near Earth's surface for an object in freefall. [7:30]