I am trying to shift my research area from Pure math to math bio for various reasons. So whatever time I invested in my algebra is not of much use plus I have to make the basics of ODE and the Dynamical system strong. I was reading Teschl's book on ODE and the Dynamical system and I felt it very hard to have a good hold on the base concept while reading the book. It is not the case that I don't understand it. Rather I can't grasp the inner concept well. I didn't read Strogatz Nonlinear Dynamics before but now I am enjoying it.
- Is there any other ODE-Dynamical system(if it is focused on oscillation theory that's a plus) undergraduate to graduate level bridging book and some books that give a deeper insight in an easier way and make the concept and problem-solving skills clearer?
- In pure math there are some books that state learning through problems and they try to build the conception with a series of easy problems. You can also refer to those books.
This will be of great help because I believe in making my base strong. Please don't suggest me a hard book. When I am finding Teschl hard and Strogatz good. You can get an idea.
E.g. I liked one undergraduate thesis on Floquet theory very helpful. It will be good if I get some easy to moderate to hard problems to solve with hints. What I really care for is learning about Existence,uniqueness, regularity Sturm Liouville, Sturm comparison theorems Linear stability, Liapunov stability, Hamiltonian, gradient systems Poincare bendixson theorem Some basic dynamical systems like omega limit sets Floquet Theory Linear ODEs etc etc.
