How did ostrogradsky prove the divergence theorem?

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SUMMARY

The divergence theorem, initially discovered by Lagrange, was later proved by both Gauss and Ostrogradsky. Each mathematician approached the proof differently, although the core principles remain consistent. The discussion highlights the challenge of finding distinct variations of the proof across different sources. It emphasizes the importance of consulting original articles and university libraries for comprehensive understanding.

PREREQUISITES
  • Understanding of the divergence theorem
  • Familiarity with the Fundamental Theorem of Calculus (FTC)
  • Knowledge of integration techniques
  • Ability to interpret historical mathematical texts
NEXT STEPS
  • Research the original papers by Lagrange, Gauss, and Ostrogradsky on the divergence theorem
  • Study the Fundamental Theorem of Calculus in detail
  • Explore different methods of proof for the divergence theorem
  • Visit university libraries to access historical mathematical literature
USEFUL FOR

Mathematicians, physics students, and anyone interested in the historical development and proofs of the divergence theorem.

semidevil
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so we know that the divergence theorem, was proved by Gauss, and also proved by ostrogradsky.

but infact, the divergence theorem was discovred by Lagrange...correct?

now, did these 3 guys prove it differently? I'm sure it couldn't be exactly the same way right? basically, I've been searching the internet all over, and can't find the differen't variations of the proof for the divergence theorem...

any help?
 
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How about trying to search over the internet the original articles and then try to find them at the closest university library...?Pay attention with Gauss,he had a weird/funny way of writing mathematics...That's what i heard.

Daniel.
 
thats an interesting question. this theorem follows so directly from the FTC plus repeated integration I cannot imagine any other way of proving it.

But whenever I say that, someone proves me wrong.
 

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