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A better way to understand Differential Equations | Nonlinear Dynamics (Part 4) | Index Theory
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....
Khan Academy
Khan Academy: Calculus: Curl 2
Video demonstrating how to calculate curl for a specific three-dimensional vector field. [10:17]
Khan Academy
Khan Academy: Calculus: Divergence 1
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]
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: Calculus: Divergence 2
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...
Khan Academy
Khan Academy: Calculus: Divergence 3
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]
Khan Academy
Khan Academy: Calculus: Curl 1
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]
Khan Academy
Khan Academy: Vector Field Line Integrals Dependent on Path Direction
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.
Khan Academy
Khan Academy: Thanksgiving Math: Green Bean Matherole
A Thanksgiving dinner compared to a vector field.
Khan Academy
Khan Academy: Viewing G as Value of Earth's Gravitational Field Near the Surface
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]