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twotwelve
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Apostol page 386, problem 5
Given [tex]f,g[/tex] continuously differentiable on open connected [tex]S[/tex] in the plane, show
[tex]\oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha}[/tex]
for any piecewise Jordan curve [tex]C[/tex].
1. Green's Theorem
2. [tex]\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}[/tex] for [tex]\nabla f,\nabla g[/tex]
I need some general direction on this one...
Homework Statement
Given [tex]f,g[/tex] continuously differentiable on open connected [tex]S[/tex] in the plane, show
[tex]\oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha}[/tex]
for any piecewise Jordan curve [tex]C[/tex].
Homework Equations
1. Green's Theorem
2. [tex]\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}[/tex] for [tex]\nabla f,\nabla g[/tex]
The Attempt at a Solution
I need some general direction on this one...
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