The goal of this paper is to present our analysis of the results of the Pre-University Educational Management (M.E.P.P.) online course, which runs over several years in the Department "Muntenia" of Continuing Education of the University of Pitesti. We have analyzing some of the aspects of this kind of the training in the online system: the organization issues concerning the Skype network, the e-learning aspects for the supports courses, the didactical communications with the participated teachers, etc. Last but not least, our study has considered also some aspects of education programs continue training for the teachers which occupies the school manager position, one of the key positions of the education system. The most important thing is the feedback which we get from our "students". This feedback allows us to improvement our activities of the training programs for the pre-university teachers and to nuance the contents and applications of the lectures for specific educational management of our educational system.

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In actual stage of the mankind, the concept of the lifelong learning is a reality of the knowledge based society because this satisfies the new needs for its complex dynamics of evolution, of transformation, of development, etc. In this framework, almost all the crafts, jobs, professions, business, social services, etc. are continuously adapting to the demands of the new human society based on "computer". By the "computer" we understand all the things and human activities which are made by /or with a computer, starting with the human common communications, through e-mail, Skype, WhatsApp, etc., till the sophistical artificial intelligences which helps mankind: to do better the things, to understand in the same time the "big" and the "little" Universe through learning. In this frame of the need of learning, it seems that the blended learning is gaining ground like a new educational paradigm which fulfils this need. Starting from a recent experience linked with a designed activity based on the blended learning technologies for reformulating a training plan of lifelong learning, which is supposed to give the school manager's competencies, dedicated for the teachers from the pre-universitary education system, if they will want to candidate at this position, this work is dedicated to some reflections about what is and what will become higher education in framework of the blended learning paradigm.

The aim of this paper is to present a comparison between the theoretical frameworks for the simulation of the movement of a vehicle in the linear case, one obtained using the exact solution of the equation of motion, and the other obtained with the solutions given by using homotopy analysis methods. Homotopy analysis methods allows the qualitative analysis of the dynamical system which is associated to a vehicle linear motion case, concerning the parameters involved in this equation of motion, for example, gears stages, adherence coefficient, aerodynamics coefficient, etc.

It is evident that the development of future generations with the right skills and knowledge, for a career in engineering at all levels, is essential for the future economic prosperity of any country. Moreover, in the future we will need professional engineers with greater interdisciplinary understanding, and with more specialist skills. So, we will need a deeper understanding of the sciences that underpin the art of engineering, and we will therefore need to know which are the mathematical skills needed to apply these sciences. Because advances in the use of information technology and computers have transformed engineering analytical techniques, production and management processes, it raises some questions: What is and will be the role of mathematics in the education of engineering? What mathematical skills are needed for the engineers of tomorrow, and how and when these might best be acquired? This paper is dedicated to an objective analysis of the positioning of mathematics courses to those of specialized training mechanical engineers. Both authors share their extensive experience in teaching mathematics and science of mechanical engineering at the Faculty of Mechanical Engineering.