In this paper we will present the eciency of the methods and the theoretical support which are applied at di erent courses and subject matters, showing the best learning way and the interaction of mathematics with new domains of research. These topics are indirect integrating in the post university, post - graduate and doctoral courses - aligned to the European reform education, which we are adhering. The themes which are presenting are reefers to: 1. Using the complex functions in the determining of the plane potential functions with singularities, these elds are encountered in hydrodynamics, electromagnetism, heat, symmetry theorems and potentials. The dynamical elds came in contact with screens, obstacles and the eld lines modify. We will give a method for the determination of the new elds and the in uence of the non-homogeneous environments. 2. Using the complex functions in elasticity are obtained new methods for the thermic potential 3. The determination of the potential spatial elds with axial symmetry knowing the potential plane elds which are generated with the complex functions. 4. Using the complex functions in the discrete dynamical systems to determine the stability criterion (the di erence equations) very useful in biology, automatics, robotics, telecommunications . In this situation the dynamic of evolution occurs in the discreet time (the second, the hour, the day, the month, the year) 5. The inverse problems and the integral equations method in the optimization