In summary, the request is for lecture notes in mathematics that are comparable in quality and content to those found on the website mathonline.wikidot.com.
No notes. But a good simple, informative, fun to read book , is book Ross : Ordinary Differential Equations.
It coveres the majority of topics in the 3rd section box, and a few from the 4th.
The only issue with Ross is that the exercises are too easy. So buy a cheap copy of Zill Ordinary Differential Equations, and work the exercises from Zill and read Ross.
For something that would cover the 4th section, it would be a second book on Differential Equations.
I dont have a recommendation, and the only book I own is the one by Arnold, readable, but advanced.