# Best Books for Ordinary Differential Equations

1. Dec 28, 2004

### Gecko

what are some of the best intros to ODEs? also, has anyone read any of the Dover books on ODEs and know which one is best? thanks.

2. Dec 28, 2004

### NeutronStar

I would strongly recommend Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard as the best introductory book I've ever read. (This is a Dover book)

It's quite extensive at over 800 pages. It's laid out in lessons instead of chapters. Each lesson has quite a few problems that can be done easily based on what has already been taught. Complete answers are given right after the problem sets in each section. It is without a doubt the very best book that I've every seen on ODEs. Especially if you are a self-learner.

It's also aimed toward scientists and engineers with practical applied examples. If you are looking for a more abstract approach with all the epsilon-delta proofs for each theory then this book is probably not for you. This is a good book if you want to understand ODE's intuitively. (Although I it doesn't water stuff down either. You get all the theorems!)

There's also a great video course on ODE's available here:
Video Differential Calculus Lecture at MIT - FREE!

I would also recommend the Schaum's Outline on ODE's which goes along well with the MIT course, and contains many interesting word problem (again, it has a lot of hands-on intuitive stuff for practical applications without loss of generality)

All of the above assumes a full knowledge and understanding of Calculus I and II, of course.

3. Dec 28, 2004

### fourier jr

"elementary differential equations" - rainville/bedient

if you're looking for cheap books (you asked about ones by dover) www.abebooks.com has a used copy of the 6th edition for US$1.00 4. Dec 29, 2004 ### Dr Transport Boyce and Diprima is a classic in the field of differential equations. 5. Dec 29, 2004 ### ReyChiquito Brown is great too 6. Dec 29, 2004 ### daster I second the Tenenbaum & Pollard recommendation! 7. Jan 5, 2005 ### rachmaninoff I need to find the Tenenbaum & Pollard, never heard of it before... I second the Boyce-DiPrima - it's very clear, and also the pictures are really great (it matters!) 8. Jan 5, 2005 ### NeutronStar Where to find Tenenbaum and Pollard ODE The Tenenbaum & Pollard book can be purchased directly from Dover books. www.doverpublication.com - Tenenbaum and Pollard ODE Or it can be found on Amazon.com on the web: Amazon Book Store the ISBN number is: 0-486-64940-7 It sells for just under$25 (under $20 at Amazon) I haven't seen the Boyce-DiPrima book but at over$100 a copy comparing it with Tenenbaum & Pollard would be like comparing apples and caviar.

Tenenbaum and Pollard is a Dover book. That's nothing to sneeze at. It is very well organized, and well written. I have yet to find a misprint, typo, or mistake (of course I haven't finished the book yet either). It doesn't contain any color pictures. All of the graphs and figures are very simple in black & white, but they convey all the information needed to make the point.

It's a small (5-3/8" x 8-1/2"), but very thick (818 pages) paperback.

I love the way that it's laid out in lesson plans. It's really aimed toward self-learners.

P.S. I'm not affiliated with this book in any way. I just love it!

9. Jan 9, 2005

### graphic7

I'm using Stephen A. Sapterstone's text this semester; it's not bad, fairly concise. I've also been using Tenenbaum & Pollard's ODE text as a suplement.

Edit: If you plan on taking numerical analysis, or you have a concentration in Applied Mathematics, I would not rely too heavily upon the numerical solutions chapter in Tenenbaum & Pollard (the original publication date is 1963). Boyce & Diprima and Saperstone have much more detailed and recent information on numerical solutions to ODEs.

Last edited: Jan 9, 2005
10. Feb 9, 2005

### kdinser

OMG, I just started reading ODE by Tenenbaum about 15 minutes ago and I can't believe how much better it is then my course text book. Where my text book obviously goes to great lengths to condense 3 or 4 concepts into one, brief, explanation and example; the authors of this book honestly take as much space as they need to.

5 minutes after opening to the chapter on linear, diff eq's of order greater then 1, it answered 5 questions that I was going to ask my professor about tonight. This book was written by a team that understands, not everyone that takes a differential equations class is planning on being a mathematician. They, not only, seem to realize that there might be 1 or 2 people out that there that didn't get straight A's in all their previous math classes, but there might be a few of us that missed an important topic here or there in our math classes. This is unlike my text book, that seems to assume that you memorized every theorem, trick, and shortcut taught in 2 semesters of algebra and 2 semesters of calculus. All I can say is THANK YOU, THANK YOU, THANK YOU, to everyone that recommended this book as a supplement.

I can't say for sure that it's the best book for everyone, but for someone like me, that seems to always get the big concepts easily and then spends hours stuck on problems because of some small, missed, detail, it is perfect.

11. Feb 9, 2005

### mathwonk

an intro de book by an eminent mathematician is the one by vladimir arnol'd. a more advanced one is by hirsch and smale,.

good dover books on d.e. include those by earl coddington (intro), and by witold hurewicz (theoretical), and I suspect the one by John Dettman is good.