Show that the Laplacian operator is isotropic (rotation invariant) Note: { x = x'Cos? - y'Sin? y = x'Sin? + y'Cos? } where (x,y) is the original coordinate system and (x',y') is the rotated system.
Added by Miriam W.
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First, we need to find the partial derivatives of the given transformation equations with respect to x and y. For fx = x'cosθ - y'sinθ, we have: ∂fx/∂x = cosθ ∂x'/∂x - sinθ ∂y'/∂x ∂fx/∂y = cosθ ∂x'/∂y - sinθ ∂y'/∂y For fy = x'sinθ + y'cosθ, we have: ∂fy/∂x = Show more…
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