Pages similar to: Green's theorem examples

The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.
When Green's theorem applies
A discussion of situations where you are allowed to use Green's theorem.
Other ways of writing Green's theorem
Small variations in the way you can write Green's theorem
Green's theorem with multiple boundary components
How Green's theorem applies even to regions with holes in them
Using Green's theorem to find area
A trick to use Green's theorem to calculate the area of a region
Calculating the formula for circulation per unit area
A sketch of the proof for the formula for the component of the curl of a vector field.
A path-dependent vector field with zero curl
A counterexample showing how a vector field could have zero curl but still fail to be conservative or path-independent.
The fundamental theorems of vector calculus
A summary of the four fundamental theorems of vector calculus and how the link different integrals.