MathStudio MathStudio Express

Jacobian(function, [varlist], [point])

[varlist]
This parameter is optional and default value is [x,y,z].

[point]
This parameter is optional and if omitted the Jacobian matrix is returned. When point is given the matrix is evaluated at that point. If point is given and the number of equations = number of variables then the Jacobian determinant is returned

Description

Returns either the Jacobian matrix or the Jacobian determinant of a function list function(varlist) evaluated at point.

Examples

Jacobian(x^2-y^2, [x, y], [u, v])
Jacobian([x^2-y^2, 2x*y, 3*x^2*y], [x, y], [a, b])
Jacobian([f(x, y, z), g(x, y, z), h(x, y, z)], [x, y, z])
Jacobian([x@_1, 5x3, 4x@_2^2-2*x@_3, x@_3*sin(x@_1)], [x@_1, x@_2, x@_3])

References

http://mathworld.wolfram.com/Jacobian.html
http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant
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