\begin{definition}[Definition:Field of Directions/Functional]
Let $\mathbf y$ be an $N$-dimensional vector.
Let the functional $J$ be such that:
:$\ds J \sqbrk {\mathbf y} = \int_a^b \map F {x, \mathbf y, \mathbf y'} \rd x $
Let the following be a family of boundary conditions, presribed $\forall x \in \closedint a b$:
:$\mathbf y' = \map {\boldsymbol \psi} {x, \mathbf y}$
Let these boundary conditions be self-adjoint and consistent $\forall x_1, x_2 \in \closedint a b$.
Then these boundary conditions are called '''field of directions''' of the functional $J$.
\end{definition}