Assorted notes on dynamical systems
Notes created for a course on
Differential equations and dynamical systems.
I wrote these up as separate notes for the spring term of 2007;
for the spring term of 2008,
I have collected the notes into one document.
The main book for the course is Jordan & Smith's
Nonlinear Ordinary Differentical Equations.
These notes serve as a supplement.
To view or download
Best for on-screen viewing: A5 size (PDF).
Best for printing: A4 size (PDF).
(If you need to print on US letter paper,
be sure to ask your printer driver to reduce the size to fit the paper.)
- Version dated 2016-03-31 (current version).
Fixed a typo: Poincaré–Bendixson requires n=2!
- Version dated 2012-03-18 (this version was never posted here).
Altered the uniqueness proof.
Corrected a typo.
- Version dated 2009-04-23.
The only difference from the previous version is that some material has
been moved to a more logical location.
- Version dated 2009-04-21.
Changes: Improved the statement and proof of Theorem 3.
In chapter 2, the argument for the saddle case is improved.
New chapter 7 on the flow.
New chapter 8, an addendum to chapter 3.
There are some cosmetic changes, including the addition of hyperlinks.
- Version dated 2009-01-12.
The only differences from the 2009-01-11 versionappear on pages 6 and 7
(3 and 4 in the A4 version): A misprint on page 7 line 8,
plus alignment of misaligned formulas.
- Version dated 2009-01-11.
The only difference from the 2008-04-03 version
results from a change in a documentclass file getting rid of a bad page break.
- Version dated 2008-04-03.
I added two new results on page 18.
This has pushed later material up to a page further back.
- Version dated 2008-01-24.
There are no major changes, but the uniqueness proof for ODEs has been improved.
There are various other minor improvements as well.
- Version dated 2008-01-11:
The first chapter, on well-posedness,
has been substantially rewritten compared to the original note.
Please respect the copyright
The notes may be freely copied for personal or classroom use;
contact me if you wish to copy them for any other reason.