  Infinitesimal variation of Action functional in classical (non-quantum) field
theory with higher derivatives is presented in terms of well-defined intrinsic
geometric objects independent of the particular field which varies.
'Integration by parts' procedure for this variation is then described in purely
formal language and is shown to consist in application of nonlinear Green
formula to the vertical differential of the Lagrangian. Euler-Lagrange
expressions and the Green operator are calculated by simple pull-backs of
certain vector bundle valued differential forms associated with the given
variational problem.
