Proofs of Stokes Theorem without Differential Forms

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SUMMARY

The discussion centers on the need for a rigorous proof of Stokes' Theorem in three dimensions without the use of differential forms. The original poster expresses frustration with existing resources that rely on differential forms, which they find unnecessary for their purposes. A reference to a specific MIT course material is provided, which includes a proof suitable for those seeking a more traditional approach to Stokes' Theorem. This resource can serve as a valuable tool for individuals looking to understand the theorem in a more accessible manner.

PREREQUISITES
  • Understanding of multivariable calculus concepts
  • Familiarity with line integrals and surface integrals
  • Basic knowledge of vector calculus
  • Ability to interpret mathematical proofs
NEXT STEPS
  • Review the MIT course material on Stokes' Theorem provided in the link
  • Study the concepts of line integrals and surface integrals in depth
  • Explore traditional proofs of vector calculus theorems
  • Investigate alternative resources that focus on calculus without differential forms
USEFUL FOR

Students of mathematics, physics enthusiasts, and educators seeking a clear understanding of Stokes' Theorem without the complexity of differential forms.

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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