Using triple integrals we can find volume between two surfaces.
About vectors in space and determining the surface vector, using flux as an example.
Whenever a force is applied to an object, causing the object to move, work is done by the force.
Divergence measures how much the flow is expanding. It singles out the stretching component of motion.
The Diffusion equation governs motion of e.g. smoke in unmovable air, or dye in a solution.
Test for gradient field. Find the potential of a gradient field.
The curl measures the value of the vector field to be conservative. For a velocity field, curl measures the rotation component of the motion.
The work done by a vector field along a closed curve, can be replaced with a double integral.
Triple integrals, surface integrals and contour integrals, and bridges between them.