Khan Academy: Calculus: Vector Field Line Integrals Dependent on Path Direction

Video lesson using line integrals to find the area along a parametric curve in both directions. Shows that the results are the same for either direction by using substitution. [16:22]

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.

Video extending the idea of a conservative vector field to show that a closed curve line integral will be equal to zero by showing that the difference of a line integral of a path and a line integral of a path with the same end points...

Using line integrals to find the work done on a particle moving through a vector field.

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 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 demonstrating how to calculate curl for a specific three-dimensional vector field. [10:17]

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...

A thorough explanation of line integration and how to represent force fields, include graphs and diagrams for visual reference and examples.

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...