Khan Academy: Calculus: Conceptual Clarification for 2 D Divergence Theorem

This video revisits the 2-D divergence theorem to involve mass density and velocity and find the mass exiting under the closed curve.

Video showing how to find the closed line integral of the dot product of a vector field and a unit normal vector to figure out how fast particles are exiting the region formed by the closed curve. Green's theorem is applied and the...

Using Green's Theorem to establish a two dimensional version of the Divergence Theorem.

Using Green's Theorem to establish a two dimensional version of the Divergence Theorem.

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...

Video lesson continuing the problem from the previous video on finding the surface area along a closed curve using line integrals. Two line integrals are set up and solved and added to the area found previously. [9:58]

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...

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]

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]

Video lesson using the washer method of integration to find the volume of a specific solid of revolution formed by two curves. [8:22]