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JacobianMatrix

JacobianMatrix[pt]
gives the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point pt.

JacobianMatrix[pt, coordsys]
gives the Jacobian matrix of the transformation from the coordinate system coordsys to the Cartesian coordinate system at the point pt.

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To use JacobianMatrix, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].

The Jacobian matrix consists of the elements m_{i, j}=_{u_j}r_i where r₁, r₂, r₃ are the Cartesian coordinates x, y, z and u₁, u₂, u₃ are the coordinates of the coordinate system coordsys, if specified, or the default coordinate system otherwise.