# 20599 Ordinary Differential Equations II 1

**Credits**: 4 advanced credits in Mathematics

**Prerequisites**: Students must fulfill all **English** requirements and take **bibliographic instruction** in the Library.

Required: Infinitesimal Calculus I, Infinitesimal Calculus II, Infinitesimal Calculus III, Linear Algebra I, Ordinary Differential Equations I, Complex Functions

Recommended: Linear Algebra II

The course, based on *Ordinary Differential Equations with Applications*, by S.-B. Hsu (World Scientific, 2006), was developed by Eli Levin, Mireille Avigal and Zippy Berger.

**Chapters**: (1) **Introduction**; (2) **Fundamental theory**: Local existence and uniqueness of solutions of IVP, continuation of solutions, continuous dependence properties, differentiability of initial conditions and parameters, differential inequalities; (3) **Linear systems**: Fundamental matrices, linear systems with constant coefficients, two-dimensional linear autonomous systems, linear systems with periodic coefficients, adjoint systems; (4) **Stability of nonlinear systems**: Definitions, linearization, orbital stability; (5) **Method of Lyapunov functions**: An introduction to dynamical systems, Lyapunov functions, simple oscillatory phenomena; (6) **Two-dimensional systems**: Poincaré-Bendixson theorem; (7) **Second order linear equations**: Sturm's comparison and Sturm-Liouville boundary value problems, distributions, Green's function, Fredholm alternative for 2nd order linear equations; **Additional topic –** **Series solutions of second order linear differential equations**: Series solution near an ordinary point and near a regular singular point, method of Frobenius, a regular singular point at infinity.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.