A definition of the exterior derivative in terms of Lie derivatives

The notion of the Lie derivative of a tensor field with respect to a vector field, though much neglected, goes back to almost the beginnings of tensor analysis. For a classical treatment see 1, pp. 72-73. A modern treatment with the simplifying assumption that the vector field does not vanish is given in 2, pp. 74-77 , but little or nothing in the way of a coordinate free treatment has appeared in print so we give an abbreviated exposition below.