Undergrad Proofs of Stokes Theorem without Differential Forms

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A request for a rigorous proof of Stokes' Theorem without using differential forms highlights a need for clarity in understanding the theorem in a 3D context. The original poster seeks a proof that is accessible and avoids the complexities of higher-dimensional calculus. They express frustration with existing resources that either use differential forms or lack comprehensive explanations. A reference to an MIT OpenCourseWare resource is provided, which may offer the desired proof. This discussion emphasizes the importance of foundational understanding in multivariable calculus for practical applications in physics.
Crek
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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.
 
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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
 

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