The main purpose of this project is to construct a particular differential algebra ρE(Ω) of generalized functions which, among other things, satisfies: (a) ρE(Ω) is an algebra of Colombeau type, i.e. ρE(Ω) contains a copy of the space D′(Ω) of Schwartz distributions (Schwartz generalized functions on an open set Ω ⊆ Rd). (b) The set of the scalars ρC of ρE(Ω) (ρC consists of the functions in ρE...