The course objectives are to learn some advanced topics in the theory of ordinary differential equations. In particular, the students are expected to master the following topics:

• Linear dynamical systems and conjugacy of linear flows;
• Autonomous systems on the plane;
• Traveling wave solutions to the reaction-diffusion systems;
• Elemenets of bifurcation theory;
• Delay differential equations.

• Classes: MWF 12:00pm-12:50pm, NDSU AGHILL CTR Building, Rm 110
• Office hours: MWF 1:00pm-1:50pm (Minard 408E22)
• Syllabus
• Textbook: No textbook is required

• 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

• Linear systems with constant coefficients
• Linear dynamical systems. Topological conjugacies
• Perron-Frobenius theorem
• Systems on the plane
• Bifurcations I
• Bifurcations II