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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