  This part of the series is devoted to the generalization of exterior
differential calculus. I give definition to the integral of a five-vector form
over a limited space-time volume of appropriate dimension; extend the notion of
the exterior derivative to the case of five-vector forms; and formulate the
corresponding analogs of the generalized Stokes theorem and of the Poincare
theorem about closed forms. I then consider the five-vector generalization of
the exterior derivative itself; prove a statement similar to the Poincare
theorem; define the corresponding five-vector generalization of flux; and
derive the analog of the formula for integration by parts. I illustrate the
ideas developed in this paper by reformulating the Lagrange formalism for
classical scalar fields in terms of five-vector forms. In conclusion, I briefly
discuss the five-vector analog of the Levi-Civita tensor and dual forms.
