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Student[MultivariateCalculus]

 Jacobian
 return the Jacobian of a list of multivariate functions

 Calling Sequence Jacobian([f(x,y,..), g(x,y,..), ..], [x, y, ..], opts) Jacobian([f(x,y,..), g(x,y,..),..], [x, y, ..] = [a, b, ..], opts)

Parameters

 [f(x, y, ..), g(x, y, ..), ..] - list (or Vector) of multivariate algebraic expressions [x, y, ..] - name; specify the independent variables a, b, .. - name or real constant; evaluate the Jacobian at the specified point opts - (optional) equation(s) of the form output=method where method is one of determinant or matrix; specify output options

Description

 • The Jacobian([f(x,y,...), g(x,y,...), ...], [x,y,...]) calling sequence returns the matrix form of the Jacobian. The calling sequence in the form Jacobian([f(x,y,...), g(x,y,...),...], [x,y,...]=[a,b,..]) returns the matrix form of the Jacobian evaluated at a point specified by $[a,b,...]$. The dimension of the point must equal the number of independent variables.
 • Specifying the option output = method returns the Jacobian in the specified form, where method is one of determinant or matrix. The matrix form is the default.
 • If the output = determinant option is given, then the number of independent variables must equal the number of algebraic expressions.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{MultivariateCalculus}}\right):$
 > $\mathrm{Jacobian}\left(\left[x+{y}^{2}\right],\left[x,y\right]\right)$
 $\left[\begin{array}{cc}{1}& {2}{}{y}\end{array}\right]$ (1)
 > $\mathrm{Jacobian}\left(\left[x+{y}^{2}\right],\left[x,y\right]=\left[1,-1\right]\right)$
 $\left[\begin{array}{cc}{1}& {-2}\end{array}\right]$ (2)
 > $\mathrm{Jacobian}\left(\left[zx+y-4,z+x-y,{z}^{2}\right],\left[x,y,z\right]=\left[1,2,C\right]\right)$
 $\left[\begin{array}{ccc}{C}& {1}& {1}\\ {1}& {-1}& {1}\\ {0}& {0}& {2}{}{C}\end{array}\right]$ (3)
 > $\mathrm{Jacobian}\left(\left[zx+y-4,z+x-y,{z}^{2}\right],\left[x,y,z\right]=\left[1,2,C\right],\mathrm{output}=\mathrm{determinant}\right)$
 ${-}{2}{}{{C}}^{{2}}{-}{2}{}{C}$ (4)
 > $\mathrm{Jacobian}\left(⟨x,x-y⟩,\left[x,y\right],\mathrm{output}=\mathrm{matrix}\right)$
 $\left[\begin{array}{cc}{1}& {0}\\ {1}& {-1}\end{array}\right]$ (5)