Proofs of Stokes Theorem without Differential Forms

[Crek]

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it.

I honestly will never use the higher dimensional version but I still want to see a full proof in the 3d case - my analysis texts use differential forms and my calculus books don't provide a real proof. I could learn differential forms but I will not use it and I will then forget, making it kind of a waste of time.

 

[jedishrfu]

Check this reference:

https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/4.-triple-integrals-and-surface-integrals-in-3-space/part-c-line-integrals-and-stokes-theorem/session-92-proof-of-stokes-theorem/MIT18_02SC_MNotes_v13.3.pdf