Differential Equations: A First Course

From a casual review of the first 300 pages or so, this looks to be a fine, well written, clear and rigorous account of basic o.d.e.s. The language is precise and articulate, the examples are displayed beautifully on the page, and there are nice pictures illustrating the geometry of phase curves and flows that is so useful in giving visual meaning to something as dry and potentially boring or repellent as a differential equation. This is probably one of my first choices for a text in a beginning college course in o.d.e. at a sophomore/junior level in the US. I have not yet taught from it, so I may change my mind somewhat when I do so, but I thought I would write this to counter the misleading review above from someone who appears to be bragging on his high school education instead of describing this book. Anyone with a modicum of acquaintance with the current textbook literature on o.d.e. knows that this is far superior to most other choices. If I am wrong, I would appreciate recommendations of better ones. Perhaps the scorn the other reviewer felt is because of the frequent statements of "FACTS" in this book as opposed to theorems with proofs. However, the FACTS and theorems here are clearly are correctly stated, and explained. And the reader who wants proofs will notice that those are actually given in exercises or in appendices of the book, and are quite rigorous and again clearly explained, or hinted at in the case of exercises. For example the existence and uniquenes theorem for first order equations, is sketched very clearly in appendix E to chapter 6, with the usual Picard fix point proof, and the linear independence of exponential solutions for differential equations, is given as an exercise. I like proofs too, but one should recognize that to merely explain clearly what is true, even without proving it, is already a useful service that many books fail to do as well this one. The fact that proofs can also be found here should eliminate the criticism anyway. The fact that it does not come with a CD ROM is a plus in my opinion, as many lesser books such as that by Devaney et al, seem to use that feature to justify charging over $130 for a poorly written, dumbed down, and verbose text. (I have a PhD in mathematics and have taught for over 40 years in college in the US, from books by Boyce and DePrima, Edwards - Penney, Coddington, Lang, Spivak, Courant, etc.) I like the first few pages of the book by Martin Braun as well, from which DeVaney et al seem to have benefited; i.e. the fun factor it embodies, and the fact that used older editions are available for under $2! perhaps in hindsight, I should grant only 4 stars to the present book to leave room for higher scores for the books below. If you want some other books that are perhaps more challenging, try the classic by Hurewicz, or the more recent beautiful one by Arnol'd. update: after choosing this book for my course, i learned it is apparently out of print, and had to sw

I have taught out of this book, and I like it very much. For its time (1992) it did a good job of beginning moving from the traditional linear approach-- with which it did a beautiful job -- to the more qualitative, non-linear approach that has now become deservedly more common.It is hard to know whether the linear algebra that students learned in using this approach was as universally useful in the later years. Certainly, a major reason for choosing the book and using that approach was to present concepts of linearization and the properties of functions and surfaces that eventually became useful in the geometry of manifolds and theoretical physics. But these are not part of the horizon of most kids studying ODE in the 21st century.The biggest factor that must contribute to the decline of the popularity of this bookmust be that it has not embraced computer algebra systems wholeheartedly. If you were to use, say Maple or Mathematica as a major tool in your course, you wouldn't find direct support for it in the book, though there would be nothing to prevent you from writing up the support materials yourself!Here's hoping that this team writes a more modern successor to this great book.Arch