ORDINARY DIFFERENTIAL EQUATIONS I

Basic concepts of ordinary differential equations. Elements from existence, uniqueness and parametric dependence theory for equations of first order. Equations of first and second order. General theory and techniques of solutions for linear equations. Applications. Qualitative theory of the solutions of the differential equation y''(x)+p(x)y'(x)+q(x)y(x) = 0 (periodic solutions, Floquet's theorem). Sturm theorems of comparison and their applications.