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.
- 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)
- Textbook: Teschl, G. Ordinary Differential Equations and Dynamical Systems, AMS, 2012, 356 pp. (Amazon) (Author's web page)
Other useful textbooks:
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