Power Series - Reference Request (?)

Question

I'm not sure if I've tagged that correctly as a reference request or not, but I'm nearly done with Kenneth Ross's book Elementary Analysis, and one of the topic's that's caught my interest to learn more about was the treatment of series, and in particular, power series. I'm fond of differential equations as a subject, and I know that there is an important relationship to studying power series and understanding many types of differential equations. I'm also particularly interested in dynamics and chaos, and am curious to seek out any connections between the two subjects, as I know that dynamic systems that arise as solutions to non-linear differential equations are not uncommon.

Does anyone have any sources that would make sense for an undergraduate just finishing their first Analysis course in either of these contexts?

Answer 1

Check this book

• Theory and Application of Infinite Series by Konrad Knopp.

Answer 2

I would suggest Principles of Mathematical Analysis by W.Rudin. It would be the next step in Analysis and he deals with power series too.

After that you might find interesting reading something in Complex Analysis and Laurent series http://en.wikipedia.org/wiki/Laurent_series. A textbook in this topic would be Complex Analysis by T.W.Gamelin.