We will use the book “Differential Equations, Dynamical Systems, and an Introduction to Chaos” by Morris W. Hirsch, Stephen Smale, and Robert L. Devaney, 3rd. edition, 2013, Academic Press.
[LEGANTO]
The lectures will be based on (subject to change)
? Chapter 1 (First-Order Equations).
? Chapter 2 (Planar Linear Systems).
? Chapter 3 (Phase Portraits for Planar Systems).
? Chapter 4 (Classification of Planar Systems).
? Chapter 5 (Higher-Dimensional Linear Algebra)
? Chapter 6 (Higher-Dimensional Linear Systems).
? Chapter 7 (Nonlinear Systems).
? Chapter 8 (Equilibria in Nonlinear Systems).
? Chapter 9 (Global Nonlinear Techniques).
? Chapter 10 (Closed Orbits and Limit Sets).
? Chapter 17 (Existence and Uniqueness Revisited).
? Numerical methods for ODEs. We use lecture notes by Ulrik Fjordholm [More].