In　this　article,　the　convergence　of　time-dependent　and　non-isentropic　Euler-Maxwell　equations　to　compressible　Euler-Poisson　equations　in　a　torus　via　the　non-relativistic　limit　is　studied.　The　local　existence　of　smooth　solutions　to　both　equations　is　proved　by　using　energy　method　for　first　order　symmetrizable　hyperbolic　systems.　The　method　of　asymptotic　expansion　and　the　symmetric　hyperbolic　property　of　the　systems　are　used　to　justify　the　convergence　of　the　limit.　(C)　2012　Elsevier　Inc.　All　rights　reserved.