In this paper, a mechanical theorem proving algorithm is proposed, which is based on the exterior differential calculation, vector formulation and the integration of the moving frames of the surfaces, geodesic frames and Frenet frames of the curves on the surfaces.

Based on the analytical solution of partial differential in symbolic differential operation,the method of dynamic mathematical modeling of a twin-spool turbojet is proposed.

Using noncommutative differential calculus,a difference complex is introduced on regular lattic and is proved to be exact by constructing homotopy maps,which is just a difference analogue of classical de Rham complex and Poincaré lemma.