Application of Green's theorem I Assume that u and u are continuously differentiable functions. Using Green's theorem, prove that [St v|dA= [ude, D where D is some domain enclosed by a simple closed curve C with positive orientation. Ur Uy

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Chapter2: Second-order Linear Odes
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Application of Green's theorem
Assume that u and u are continuously differentiable functions. Using Green's theorem,
prove that
JS
D
Ur
Vy
dA=
u dv,
where D is some domain enclosed by a simple closed curve C with positive orientation.
Transcribed Image Text:Application of Green's theorem Assume that u and u are continuously differentiable functions. Using Green's theorem, prove that JS D Ur Vy dA= u dv, where D is some domain enclosed by a simple closed curve C with positive orientation.
Expert Solution
Step 1

Given:

It is given that u and v are continuously differentiable functions.

 

To Prove:

DuxvxuyvydA=Cudv using Green's Theorem, where D is some domain enclosed by a simple closed curve C with positive orientation.

 

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