Courses

Basic concepts of SDEs. SDEs of first order of separable variables and categories of SDEs reduced to them. Complete SDEs of first order and Euler multipliers. Linear SDEs of first order, Bernoulli SDEs, Riccati SDEs. Applications: modeling and solving problems that result in SDEs of first order from various sciences. Qualitative analysis, through graphical representations of SDE solutions, orthogonal trajectories. Picard's theorem for the existence and uniqueness of the solution to the initial value problem y΄(x) = f(x,y), y(x0) = y0. General theory of linear SDEs of order n ≥ 2. Solving linear SDEs. of order n ≥ 2, with constant homogeneous and non-homogeneous coefficients. Euler-Cauchy S.D.E. and techniques for solving linear S.D.E. of the second order with non-constant coefficients. Applications: free and forced oscillations and other problems that result in S.D.E. of order n ≥ 2. Linear systems of two coupled S.D.E. of the first order. In order to highlight the special elements of pedagogical and teaching competence contained in the course, emphasis is placed on its historical development, the development of its cognitive subject, but also on its applications in technology and/or other sciences.