  By generalizing the cosymplectic setting for time-dependent Lagrangian
mechanics, we propose a geometric framework for the Lagrangian formulation of
classical field theories with a Lagrangian depending on the independent
variables. For that purpose we consider the first order jet bundles $J^1\pi$ of
a fiber bundle $\pi:E\to {\mathbb R}^k$ where ${\mathbb R}^k$ is the space of
independent variables. Generalized symmetries of the Lagrangian are introduced
and the corresponding Noether Theorem is proved.
