Syllabus
1) the theory of ordinary differential equations; the notion of Caratheodory solution and its existence and uniqueness, continuous dependence on the initial datum, linear equations in a Euclidean space-structure of solutions, the fundamental matrix, variation of constants 2) the theory of linear partial differential equations; 1st order equations, the method of characteristics, classification of equations of the 2nd order, parabolic equations (the Cauchy problem, an outline of basic boundary value problems, the notion of Green function), elliptic equations (an outline of basic boundary value problems).
Annotation
In the lecture, some selected chapters from the theory of differential equations are dealt with. In particular, in the theory of ordinary differential equations: the notion of Caratheodory solution and its existence and uniqueness, continuous dependence on the initial datum, linear equations in a Euclidean space-structure of solutions, the fundamental matrix, variation of constants; in the theory of linear partial differential equations: 1st order equations, the method of characteristics, classification of equations of the 2nd order, parabolic equations, elliptic equations.