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.

__Classes:__MWF 1:00pm-1:50pm, NDSU Minard Hall Room 208__Office hours:__MWF 9:00am-10:00am (Minard 408E32) or by appointment (in my office or through Zoom)- Syllabus
__Textbook:__Teschl, G. Ordinary Differential Equations and Dynamical Systems, AMS, 2012, 356 pp. (Amazon) (Author's web page)

- Chapter 1: Introduction
- Chapter 2: Fundamental Theorems
- Chapter 3: Linear systems
- Chapter 4: Stability
- Chapter 5: Boundary value problem (updated on 12.04.19)

- Ordinary differential equations by Arnold, V.I.
- Differential Equations, Dynamical Systems, and Linear Algebra by Morris W. Hirsch and Stephen Smale, first(!) edition
- Theory of Ordinary Differential Equations by Earl A. Coddington and Norman Levinson
- Ordinary Differential Equations by Philip Hartman
- Ordinary Differential Equations by Jack K. Hale
- Differential Equations and Dynamical Systems by Lawrence Perko
- Theory of Ordinary Differential Equations by Christopher P. Grant, lecture notes

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