Determinants {Jacobian determinant} {functional determinant} can be for coordinate transformations: double integral of F(x,y) * dx * dy = double integral of G(u,v) * determinant(fu, fv, gu, gv) * du * dv. Jacobian determinants have two rows of partial derivatives, one row for F(x,y) and one row for G(u,v). Jacobian determines scalar for unit vectors. Jacobians can determine normal vectors at function intersections.
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Date Modified: 2022.0224