1. Using surface integrals
Surface area
Surface integrals of scalar functions
Flux integrals
Alternative notations and some proofs (optional)


2. Understanding and using Green's theorem
Green's theorem in simply connected regions
Green's theorem in multiply connected regions
Interpretations of Green's theorem
Irrotational and incompressible flow
Sufficient conditions for the existence of a potential function


3. Understanding and using Stoke's theorem
The meaning and plausibility of Stokes' theorem
A plausibility argument for Stokes' theorem (optional)


4. Understanding and using Gauss' theorem
The meaning and plausibility of Gauss' theorem
A plausibility argument for Gauss' theorem (optional)


Index.