2D Measurements
integrating tangential and normal components of vector field for flow; recognizing clockwise/counterclockwise and inward/outward from sign and parametrization
general path integrals
flow integrals for spotting sources and sinks
gradient fields are very special vector fields: independence of path, fundamental theorem of path integrals, net flow-along closed curves is zero

2D Integrals
definition of 2D integrals
computation by slicing
computation by Gauss-Green
recognizing which method to use
area of region as 2D integral
average value of a function on a region
centroid of a region
probabilities given a 2D distribution

Sources, Sinks, Swirls, and Singularities
divergence and connection to sources, sinks, and flow across
rotation/curl and connection to swirls and flow along
singularities as big sources/sinks
Gauss-Green and its relationship with path integrals

Transform 2D Integrals
transformations of the plane, a.k.a. change of coordinates
area conversion factor, a.k.a. the Jacobian
transforming 2D integrals
finding a transformation to make a 2D integral easier
density, mass, and area of flat plates