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Proof of Stokes' theorem

7 videos
You know what Stokes' theorem is and how to apply it, but are craving for some real proof that it is true. Well, you've found the right tutorial!

Stokes' theorem proof part 1

VIDEO 5:14 minutes
The beginning of a proof of Stokes' theorem for a special class of surfaces. Finding the curl of our vector field.

Stokes' theorem proof part 2

VIDEO 7:39 minutes
Figuring out a parameterization of our surface and representing dS

Stokes' theorem proof part 3

VIDEO 4:11 minutes
Writing our surface integral as a double integral over the domain of our parameters

Stokes' theorem proof part 4

VIDEO 7:19 minutes
Starting to work on the line integral about the surface

Stokes' theorem proof part 5

VIDEO 5:28 minutes
Working on the integrals...

Stokes' theorem proof part 6

VIDEO 5:27 minutes
More manipulating the integrals...

Stokes' theorem proof part 7

VIDEO 11:49 minutes
Using Green's Theorem to complete the proof