Overview Triple integrals, surface integrals and contour integrals, and bridges between them.

Stokes’ for work (in space) The work done by a vector field along a closed curve, can be replaced with a double integral.

Curl (in space) The curl measures the value of the vector field to be conservative. For a velocity field, curl measures the rotation component of the motion.

Gradient Field (in space) Test for gradient field. Find the potential of a gradient field.

Diffusion/heat (in space) The Diffusion equation governs motion of e.g. smoke in unmovable air, or dye in a solution.

Divergence (in space) Divergence measures how much the flow is expanding. It singles out the stretching component of motion.

Work (in space) Whenever a force is applied to an object, causing the object to move, work is done by the force.

Vector Fields; Surface integrals; Flux (in space) About vectors in space and determining the surface vector, using flux as an example.

Triple Integrals Using triple integrals we can find volume between two surfaces.