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.