# Math 716, Ordinary Differential Equations

## spring 2020

**Instructor**
Sigurd Angenent, Van Vleck hall 609.

**Prerequisites**
A thorough understanding of undergraduate real analysis (e.g. as in chapters 1—9 of Rudin’s Principles of Mathematical Analysis.)

**Topics**
- Existence and uniqueness theorems for diffeqs in $\R^n$
- Stable, unstable, and center manifolds of fixed points; bifurcation theory point of view.
- Topological dynamics (flows, invariant sets, recurrence)
- Poincaré—Bendixon theorem
- Chaotic dynamics (Poincaré’s homoclinic tangle and Smale's horseshoe in various concrete examples).

**Homework** There will be short homework assignments every other week.

**Exams** There will be one midterm exam, and one final
exam. Both will be take home exams.

**Textbook** We will very loosely follow the book by Luis Barreira and Claudia Valls,

*Ordinary Differential Equations (Qualitative Theory)*, 1st edition, AMS Graduate Studies in Mathematics, volume 137.

Book website