Notes on numerical methods
This set of notes on numerical methods for ODEs [updated 01.05.2018]. Please let me know if you find any errors!
Differential Dynamical Systems
Most of the material on dynamical systems will be taken from
James D. Meiss: Differential Dynamical Systems, Revised Edition. Published by SIAM (2017). ISBN: 978-1-61197-463-8
A rough overview of the relevant chapters is listed here. Note, however, that the syllabus in this course will be everything that is taught in the lectures.
- Chapter 1: Most of the material here.
- Chapter 2: Sections 2.1–2.7, but note:
- Sec 2.3: Everything up to (but not including) Example 2.10. In class I talked about the exponential of matrices, not operators, but there is no essential difference. I did not talk about nilpotent matrices.
- Sec 2.6: I only briefly talked about the case of eigenvalues with higher algebraic multiplicity. You should have an idea of how the solution looks like in the 2D case (using the Jordan normal form).
- Chapter 3: The whole chapter. I will teach this material with far less rigour and details than what's found in the book. You should understand the main ideas and techniques used, without necessarily understanding all of the technical details. You should be able to tell whether an ODE has a unique solution, say, if \(f\) is Lipschitz continuous.
- Chapter 4: Section 4.1–4.8.