  In this paper, we generalize De Donder approach to construct boundary forms
that depend on the adapted coordinate system used. In continuum mechanics, use
of boundary forms leads to splitting of the total force acting on the body into
body force and surface traction. Moreover, this splitting is independent of the
choice of the boundary form used. In calculus of variations, use of boundary
forms leads to equations in exterior differential forms that are equivalent to
the Euler-Lagrange equations. Infinitesimal symmetries of the theory lead to
conservation laws valid for any choice of the boundary form used. In an
example, we show that the boundary conditions lead to independence of constants
of motion of the choice of the boundary form.
