Note that this course requires that you know some linear algebra and nonlinear dynamics. I will give you a good intro to the latter but you may want to look at some other books for more help. I recommend:
I will also be doing some perturbation theory. The book by Jim Keener Principles of Applied Math is excellent for this.
You will also be required at some points to do some numerical stuff such as calculating phaseplanes, bifurcation diagrams, and possibly solving boundary value problems. For this, I recommend XPPAUT which runs on most platforms. If you prefer, there are other packages that are similar such as the Python interface to AUTO, PyDstool, and Matcont which works with MATLAB. As needed, I will provide some guidance here.
There are typos in the HW 3. Here they are: