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The class that I'm taking is called, Intermediate Ordinary Differential Equations and our required textbook is called Differential equations, Dynamical Systems and an Introduction to Chaos by Morris W. Hirsch, Stephen Smale and Robert L. Devaney. I'm hoping that I can get some good suggestions on books that can provide more detailed detailed descriptions of some of the material with more concrete examples. I'm not a math major so I don't have as much experience with using fancy math language as some people and I tend to need some good examples to concrete the idea's in my head. I find that a lot of textbooks, for me anyway, seem to be written in a way that if you understand the material they're great but if your trying to learn from them it's kind of a pain, at least in these higher level courses.

Any suggestions would be great I love looking at different textbooks because usually between a couple of them I can piece together what is going on.

Thank you!

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You might want to take a look at Vladimir Arnol'd's Ordinary Differential Equations. Arnol'd opposed the typical theorem-proof style of writing math text books, and liked to present many concrete examples, typically drawn from physics. His books are filled with numerous explanations that try to give deep geometric and physical insight into the subject matter.

Now, there is a lot of deep mathematics in this book. If you tried to make everything rigorous that he presents using physical reasoning, it would send you deep down the rabbit-hole. If you ever finished you'd probably be able to call yourself a mathematician. However, I personally found reading this book to be very valuable, even though I didn't understand all of the details. I recommend it to anyone who wants a deeper understanding of the material you typically see in an undergraduate ordinary differential equations class.

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  • $\begingroup$ I found an ancient copy of this text in my university library from 1973. It actually looks pretty good, like a if you took the advanced calc class I took and mashed it together with the ODE class I'm taking now. Thanks I'll definitely take a closer look at this book while I have some time. $\endgroup$ – Jordan Feb 21 '13 at 2:13
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Steven Strogatz book on nonlinear dynamics has plenty of examples, and could be a good companion to the textbook you mentioned (which is a great book btw).

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  • $\begingroup$ Thank you, it's funny because I have some friends that are taking a class called Nonlinear Dynamical Systems and Chaos and they actually use this text. I'll see if I can borrow it from one of them. Thank you! $\endgroup$ – Jordan Feb 21 '13 at 1:44

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