Help in proof (Green's Theorem)

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SUMMARY

The discussion centers on proving Green's Theorem, specifically the application of the Divergence Theorem to derive the necessary equations. The user has attempted to express the vector field as u = u1 i + u2 j and has successfully calculated the divergence but is struggling to progress further in the proof. Key equations related to the theorem were referenced but not explicitly detailed in the discussion.

PREREQUISITES
  • Understanding of Green's Theorem and its applications
  • Familiarity with the Divergence Theorem
  • Knowledge of vector calculus, specifically divergence and curl
  • Ability to manipulate vector fields in two dimensions
NEXT STEPS
  • Review the proof of Green's Theorem in detail
  • Study the Divergence Theorem and its relationship to Green's Theorem
  • Practice problems involving vector fields and their divergences
  • Explore examples of applying Green's Theorem to various regions
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Students studying vector calculus, particularly those tackling proofs involving Green's Theorem and the Divergence Theorem, as well as educators seeking to clarify these concepts for their students.

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Homework Statement



I have a doubt in proving the attached theorem. I have found that divergence theorem can be applied. However I am not able to arrive at the exact equation.

Homework Equations



Attached

The Attempt at a Solution



Derived the LHS. Couldn't proceed from there.
 
Last edited:
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I consider u to be u1 i + u2 j and found the divergence. How to proceed from there?
 

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