Jacobian
The
Jacobian
is the
n×n matrix
of partial derivatives of the entries in a vector field
f1
x1,
x2,…,
xn
,
f2
x1,
x2,…,
xn
,…,
fn
x1,
x2,…,
xn
Jacobians resemble Hessians in that the order of the variables in the
variable list determines the order of the columns of the matrix, and
lexicographic order is usually correct. The number of variables should be
the same as the dimension of the vector; if they are not the same, either a
parameter has been included in the variable list, or the vector field is
independent of one of the variables. In this case, a dialog box asks for the
list of variables. In each of the following examples, the variable list is x, y, z. To verify these examples, choose Jacobian while the
insertion point is in the given vector field.
Vector Calculus + Jacobian
(yz, xz, xy), Jacobian is


6pt
(x2z, x + z, xz2), Jacobian is


6pt (y is missing)
(x2z, y + c, yz2), Jacobian is


(c is extra)