I am an engineering student and I need to acquire a good understanding of some notions in differential geometry such as manifolds, diffeomorphisms, distributions, etc. I can't find a proper starting path. How should I start to learn the subject from basics?
I need the material to study geometric nonlinear control theory. Any further suggestions are appreciated.
Best Answer
In case someone else in a search comes across this question. If you want to learn it for nonlinear control purposes, Nonlinear dynamical control systems by Nijmeijer and van der Schaft gives a nice introduction plus you clearly see where what is used, like Frobenius' theorem. Now if you what learn more about differential geometry I would suggest reading any book by John M. Lee, especially Introduction to Smooth Manifolds. Then If you want to continue, people like Jerrold Marsden, Hector Sussmann and Andrew Lewis all have fantastic material related to geometric control. Especially the book Manifolds, Tensor Analysis and Applications contains, I believe, close to all the mathematics related to control and dynamical systems, from a geometric point of view.