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Jacobian

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Jacobian [dʒəˈkəʊbɪən], Jacobian determinant
n
(Mathematics) Maths a function from n equations in n variables whose value at any point is the n x n determinant of the partial derivatives of those equations evaluated at that point
[named after Karl Gustav Jacob Jacobi (1804-51), German mathematician.]


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n] indicates the volume of the element n, (x,y,z) are the co-ordinates in the CT reference system, (r,s,t) are the local co-ordinates in the element reference system, and J represents the Jacobian of the transformation.
We also assume that the determinant of the Jacobian matrix is positive, guaranteeing uniqueness of the equilibrium.
 
 
 
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