All references are to R. C. Robinson's book, if not otherwise specified. Please remember that Robinson's book puts all of the theory in the last section of each chapter. I consider these sections the most important, even when I don't explicitly mention it below!
Chapter 1
Everything.
Chapter 2
You can skip:
- The part on the Wronskian W(t)
- The existence and uniqueness of solutions of linear systems (Lemma 2.8, Thm 2.1, Thm 2.10), since we will do it more generally in Chapter 3
- The discussion leading up to Thm 2.15 deals with A possibly not diagonalizable. You can read this if you want to, but I only consider the version with A diagonalizable (like I did in class) important for the exam.
- Skip the section on quasiperiodic equations in Section 2.5.
Even though I do not go through the examples in Section 2.4, it's a good idea to read them to get a better feel for the theory.
Chapter 3
The entire chapter. I proved existence, uniqueness and stability assuming global Lipschitz continuity, while the book only assumes local Lipschitz continuity (and hence only gets local existence, i.e. up to some finite time). The book also assumes continuous differentiability of F, but this is more or less the same as Lipschitz continuity.