We introduce Stokes’ theorem.

Nevertheless, once we know Stokes’ theorem, we can view it as a direct generalization of Green’s theorem.

If we compare the conclusion of Stokes’ theorem to the conclusion of Green’s theorem, we see that they are quite similar: Like Green’s theorem, Stokes’ theorem compute circulation along a surface:

### Transforming integrals

Like the divergence theorem, one application of Stokes’ theorem is to transform a difficult integral into an easier one.

### Swapping surfaces

Since Stokes’ theorem says that if we want to evaluate the circulation along
a surface, we need only look at the boundary, we can sometimes be very
clever, and swap one surface for another, provided that they have the *same*
boundary!

### Our final fundamental theorem of calculus

How is Stokes’ Theorem a fundamental theorem of calculus? Well consider this:

Are there no more fundamental theorems of calculus? Well, there are, but as you will see if you continue your study of mathematics, they are all generalizations of the theorems we already know.

For some interesting extra reading check out: