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

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We are going to find the solution of the following integral:ʃxydy-y ^{2}dxalong the square with corners (0,0), (1,0), (1,1), (0,1). The normal form of Green's theorem: ʃF·nds = ʃF _{1}dy-F_{2}dx = ʃʃ∇·FdAWe are using the normal form of the Green's theorem with the vector field: F = [F _{1},F_{2}] = [xy,y^{2}]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-y ^{2}dxalong the square with corners (0,0), (1,0), (1,1), (0,1). The tangential form of Green's theorem: ʃF·Tds = ʃF _{1}dx+F_{2}dy = ʃʃ(∇xF)·kdAWe are using the tangential form of the Green's theorem with the vector field: F = [F _{1},F_{2}] = [-y^{2},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. |