Example 1.
We initialize a 3-dimensional manifold with coordinates [x, y, z].
We use the declare command in PDEtools to display the partial derivatives of the functions a(x, y, z), b(x, y, z) and c(x, y, z) in compact form.
The exterior derivative of a function:
The exterior derivative of a 1-form:
The exterior derivative of a 2-form:
Example 2.
By way of an example, we illustrate the fact that d^2 = 0.
Example 3.
The ExteriorDerivative command can also be applied to a list of forms or a matrix of forms.
Example 4.
The ExteriorDerivative command can also be used with adapted frames. First we define an adapted coframe for M.
Example 5.
The ExteriorDerivative command can be used with Lie algebras.
Example 6.
The ExteriorDerivative command can also be used with abstract differential forms.