In the frame of ECCUM project the two weeks training on mathematical engineering for TTPU staff was held on 9-20 of October 2017. Training was provided by Professor Stefano Berrone (Politecnico di Torino). The main topics of the training were: Heat and elasticity equations, Variational formulation of Sobolev spaces, Discrete variational formulation, stability and convergence, Triangular meshes and P1element assembling, H1 and L2 error esimates, Effect on the mesh quality on the approximation of solutions, P2 elements, Mesh adaptivity and a posterior error estimates, FreeFem++, Discussion of applicative problems and possible research topics.