3D Integrals and Transformations, Spherical Coordinates

definition as Riemann sum
volume is triple integral of 1
computing via slicing/sticks
changing order of integration
transformations
spherical coordinates


3D Flow-Across

surface integrals: scalar and flow-across
Gauss's theorem in 3D (a.k.a. Divergence Theorem)
replacement surfaces
sources, sinks, singularities in 3D vector fields


3D Flow-Along

3D flow along curves
3D gradient fields, Fundamental Theorem of Line Integrals in 3D
curl of a vector field: computation, meaning
Stokes's theorem
replacement surfaces