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In the fall I will be teaching an intro to diff.eq.s course for undergrad engineers. The usual textbook is $150 with solution manual and it's not that great. There must be a cheaper alternative that's just as good. Any help would be greatly appreciated.

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community-wiki'd. – Scott Morrison Apr 19 '10 at 19:50

I cut my teeth on an 80's version of Differential Equations and Their Applications: An Introduction to Applied Mathematics by Martin Braun . Amazon lists copies as going for under $50. Perhaps someone from this millenium can say if the new editions are still good. I liked the anecdote about the Tacoma Narrows Bridge, and found many of his examples well motivated.

Gerhard "Ask Me About System Design" Paseman, 2010.04.15

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Yes, Braun's book is great for someone meeting differential equations systematically for the first time. I used it freshman year in college. We actually used an abridged form of Braun's book called "Differential Equations and Their Applications, Short Version". I don't know if that short version is published anymore. It is not overly expensive. – KConrad Apr 16 '10 at 18:31
Rigorous, entertaining, and clear. I used this successfully and felt it a gift to be able to motivate my students with examples like his story of scientists spotting fake "old masters'" paintings by dating the age of the paint, Tacoma narrows bridge "galloping gertie", and the increase of the shark population in an Italian harbor during WW2. NOt to mention entertaining accounts of the shape of the table at the Vietnam peach talks. It reminded of an Oliphant? cartoon of the period which depicted the cartoonists' solution, a revolving table suspended from a light fixture. – roy smith May 13 '11 at 1:18
my apologies for the caps. this happens when my fat fingers stumble over the keys. – roy smith May 13 '11 at 1:20

I could do worse than to direct you to Dover Publications. They have at least half a dozen introductory differential equation books, all for less than $50.

This one has good reviews and it's only $25: Ordinary Differential Equations by Morris Tenenbaum & Harry Pollard

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I liked Coddington's textbook from Dover. (Without Levinson...) At the end I added a bit on Laplace transform. – Gerald Edgar Apr 15 '10 at 19:59
Coddington is one of the WORST textbooks in the history of the subject. IT HAS NO APPLICATIONS! That's like trying to do King Kong without the ape....... – The Mathemagician Apr 15 '10 at 21:09
Another classic book is Hirsh and Smale:… – Miguel Apr 21 '10 at 23:25
+1'd this, Dover is a reasonable alternative, though the notation can sometimes be difficult to parse. Also some are terribly typeset, but they're Well worth the investigation – Michael Hoffman Jul 12 '10 at 19:25
Tenenbaum and Pollard is indeed outstanding. Good workable examples, a correct definition of a differential, and solutions techniques I had never seen elsewhere. I posted a review (as mathwonk) on Amazon after using it for a course. – roy smith May 13 '11 at 1:10

Ordinary or Partial differential equations? It may also help if you tell us what the outrageously expensive book is so we can better recommend a book of similar level. (You are not speaking of Birkhoff and Rota, are you? I know that one is about the price you listed.)

For ODEs, I'd recommend V.I. Arnold's book, it is a classic and under USD30 on Amazon for the paperback edition. Slightly more expensive is Philip Hartman's book, which also covers more material. I bought it many years ago, new, for under USD40, so I am not quite sure what's up with Amazon now that the Hardcover is listed for USD38, while the paperback for close to USD70.

For PDEs, McOwen's Partial Differential Equations: Methods and Applications is not bad at USD60, though its 1st order nonlinear system section is a little bit confusing.

(A bit of meta gripe: using multiple dollar signs in one paragraph seems to trigger math mode when it really oughtn't, which is why I wrote "USD" above for U.S. Dollars.)

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Those books are probably way too hard for what he wants,Willie. – The Mathemagician Apr 15 '10 at 21:02
Arnold's book is not suitable for engineers, who want to learn how to solve ODEs practically. – KConrad Apr 16 '10 at 15:53
The Arnol'd book is sophisticated, but is the only one i know to make ode intuitively understandable. I.e. good for advanced students (like me) who never "got" ode. – roy smith May 13 '11 at 1:11

The best undergraduate introduction to differential equations I know-which would be wonderful for your course and you could probably get second hand cheap-is George Simmons' DIFFERENTIAL EQUATIONS WITH HISTORICAL NOTES AND APPLICATIONS.It's not too rigorous (although it's done carefully),has lots of applications and even better,it's one of the most beautifully written mathematics books ever published.It almost reads like a novel,with Simmon's wonderful humor and amazing knowledge of the history of the subject. It really makes the subject come alive and your class will love it.

Don't get the revision with Steven G. Krantz. Not only is it a lot more expensive,that book is a lot more formal and a lot of Simmons' personal touch that made the first one a classic is utterly missing here. Get either the first or the second edition of the original.

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This is out of print and so is probably unsuitable as a textbook for a course, unless your university bookstore director says otherwise. – Nate Eldredge Apr 15 '10 at 21:47
I'm sure there are enough copies floating around online to use it for a course,Nate.Probably cheap,too. – The Mathemagician Apr 16 '10 at 3:57
-1, all caps shouting. – Scott Morrison Apr 19 '10 at 19:50
@scott. You ARE kidding,right? I cannot believe this.......... – The Mathemagician Apr 20 '10 at 2:25
You're right: I should have just edited (which I've done now). I just wanted to call attention to the fact that all caps on the internet is generally interpreted as shouting, and so inappropriate here. I wouldn't shout at tea, so you probably shouldn't shout here. Looking through the database, there are only ~5 previous examples of sentences in all caps. – Scott Morrison Apr 20 '10 at 15:54

my favorite ode books for teaching are the ones by either tenenbaum and pollard, or martin braun. these are cheap and excellent. of course arnol'd is incredible but at a higher level. good for me and you, perhaps.

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If the students at your College/University own the Stewart Calculus book, chapters 9 and 17 are probably a good place to start. Or at least to suggest as a supplement to the primary text you choose.

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+1'd this, Stewart's book is quite good and it is a good place to start if nothing else, since your students probably already own it – Michael Hoffman Jul 12 '10 at 19:26

Wow, how did this old question get resurrected? Anyway, there is something I don't see in any of the other answers, so I'll chime in:

Unlike Calculus, one of the problem I find with the Diff Eq is that there is no canonical syllabus. So unless U of Saskatchewan does have a very fixed syllabus for the course, the first step is to decide what "flavor" of course you want. For instance, I had a look at a few of the Dover books, but they seem weak if you want a more "modern" (i.e. technology-based / more pictures) approach to ODE's. Which BTW might be the right way to go especially for engineers.

I have yet to find a book that fits my needs, not have I managed to completely pin down what the ideal syllabus should be.

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my apologies for not noticing all my suggestions were already here. but at least it motivated your good observation. – roy smith May 12 '11 at 20:58

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