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