Ordinary Differential Equations

Ordinary differential equations- first order equations, Picard’s theorem (existence and uniqueness of solution to first order ordinary differential equation). Second order differential equations- second order linear differential equations with constant coefficients. Systems of first order differential equations, equations with regular singular points, stability of linear systems. Introduction to power series and power series solutions. Special ordinary differential equations arising in physics and some special functions (e.g. Bessel’s functions, Legendre polynomials, Gamma functions) and their orthogonality. Oscillations - Sturm Liouville theory.