One of the most interesting applications of ODEs (in my opinion) is the field of control theory, which empowers autonomous systems/robots/vehicles to guide them

One of the most interesting applications of ODEs (in my opinion) is the field of control theory, which empowers autonomous systems/robots/vehicles to guide themselves. Brian Douglas has some fantastic introductory videos on the subject [1]. I don't think I agree completely with section 5 (Forget About Existence and Uniqueness of Solutions). For an ODE in the form xdot = f(t,x), existence and uniqueness on an interval follows if f is continuous in t and Lipschitz continuous in x [2]. This often isn't too difficult to demonstrate for a given system. In addition, if you can't prove uniqueness of solutions then you likely have to treat the system as a differential inclusion [3]. I personally find differential inclusions fascinating, but the math can be much more dense. [1]: https://engineeringmedia.com/videos https://engineeringmedia.com/videos [2]: https://en.m.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem https://en.m.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f... [3]: https://en.m.wikipedia.org/wiki/Differential_inclusion https://en.m.wikipedia.org/wiki/Differential_inclusion