SimReal: Mathematics - Vector Calculus - Green's Theorem - Example 001 | ![]() |
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. |