Ordinary Differential Equations I: Math 760

The course objectives are to learn the basics of a rigorous theory of ordinary differential equations. In particular, the students are expected to master the following topics:

• General theory. General uniqueness and existence results. Well-posed problems. Grownwall's inequality. Dependence on the initial conditions and parameters.

• Linear systems. Fundamental solutions. Matrix exponent. Solutions of linear systems with constant coefficients. Linear systems with periodic coefficients.

• Stability. Definitions. Lyapunov functions. Autonomous systems. Dynamical systems.

• Boundary Value Problem. Spectral theory of compact self-adjoint operators. Regular Sturm–Liouville problems.