I am currently an undergrad math major taking a gap year (because my university is entirely online this semester). For this year, I have signed up for a "Directed Reading Program" with a graduate student whose specialty involves dynamical systems. For this program, I am supposed to read through a textbook that we can discuss. Two of her suggestions were Nonlinear Dynamics and Chaos by Steven H. Strogatz and Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch, Smale, and Devaney.
As I took a look at those books, I realized an additional reason why reading a book such as those could be useful: although I took a differential equations course at my local community college when I was in high school, I don't remember them all that well. My university's math department is very theory-oriented, so I may never have the opportunity to take a DiffEQ course as an undergrad, though, as a math major who may want to go into something more applied, I feel as though a high level of comfort with differential equations would be nice to have. Looking through the two textbooks online, neither appears to cover Laplace transforms, which I remember to have been an entire unit in my community-college course. Because of this, I am having doubts about the efficacy of the two books with respect to giving me said comfort. However, the books seem to be fantastic with respect to gaining a deeper understanding of the material, so I am not trying to criticize.
- Between Strogatz and Hirsch/Smale/Devaney, which would you recommend?
- In light of the above (the lack of coverage of topics such as Laplace transforms), do you think I ought to, in addition to one of those two books, spend time with Ordinary Differential Equations by Tenenbaum and Pollard (which I got for Christmas or something awhile back but haven't spent much time with)?