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Student[MultivariateCalculus]

  

Jacobian

  

return the Jacobian of a list of multivariate functions

 

Calling Sequence

Parameters

Description

Examples

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

withStudent[MultivariateCalculus]:

Jacobianx+y2,x,y

12y

(1)

Jacobianx+y2,x,y=1,1

12

(2)

Jacobianzx+y4,z+xy,z2,x,y,z=1,2,C

C11111002C

(3)

Jacobianzx+y4,z+xy,z2,x,y,z=1,2,C,output=determinant

2C22C

(4)

Jacobianx,xy,x,y,output=matrix

1011

(5)

See Also

Student

Student[MultivariateCalculus]

 


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