SimReal: Mathematics - Vector Calculus - Green's Theorem - Example 001 UiA Logo

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We are going to find the solution of the following integral:
ʃxydy-y2dx
along the square with corners (0,0), (1,0), (1,1), (0,1).



The normal form of Green's theorem:
ʃF·nds = ʃF1dy-F2dx = ʃʃ∇·FdA

We are using the normal form of the Green's theorem with the vector field:
F = [F1,F2] = [xy,y2]



Use the big scrollbar in the simulation window to compute the left side of Green's theorem and convince yourself that the answer is 3/2.

Mark the checkbox 'CurlDiv' to visualize the computation of the right side of Green's theorem and convince yourself that this will give the same answer.

We are going to find the solution of the following integral:
ʃxydy-y2dx
along the square with corners (0,0), (1,0), (1,1), (0,1).



The tangential form of Green's theorem:
ʃF·Tds = ʃF1dx+F2dy = ʃʃ(∇xF)·kdA

We are using the tangential form of the Green's theorem with the vector field:
F = [F1,F2] = [-y2,xy]



Use the big scrollbar in the simulation window to compute the left side of Green's theorem and convince yourself that the answer is 3/2.

Mark the checkbox 'CurlDiv' to visualize the computation of the right side of Green's theorem and convince yourself that this will give the same answer.

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