Ordinary Differential Equations (Dover Books on Mathematics)

I took ODE this semester, and I was liking the subject until I got to read the textbooks assigned to it. It is impressive how the world is filled with giant text books that are absolutely dull and useless and extremely expensive. Luckly I have always been fond of Amazon, so I searched "Ordinary Differential Equations" and came upon this book, which at first glance looks tiny and unpromising, but trust me, this little beast doesn't only talk about ODE, it takes the subject, makes it its own, and in the most elegant of fashions transmits the knowledge so well that it even if I live in Ecuador and English is only my second language, I could grasp all what was necessary to, not only pass ODE, but to take my knowledge and apply it to computer programming right away. Trust me, if a book teaches so well that you can go ahead and apply it just like that, it is something special. Now strictly speaking on it's qualities: First, the book is a breeze to read, you will not find yourself reading back again through the text because of the lack of good pedagogy, but be aware, the writer does not bother to make you laugh either (a quality most serious books should not have, but I like what Stephen Prata did on C++ Primer Plus). Secondly, Ordinary Differential Equations has all that you will probably need for the subject. Check the MIT Open Course Ware, I downloaded the exams on the web page and did them singlehandedly, only with what this book taught me. Actually, you'll see lots of other topics that MIT doesn't even cover, for example it has a very interesting section on numerical methods. Something that has to be mentioned is that this book covers a great amount of material in a excellent order and pace. The writer never assumes that you are a genius on calculus, so he always makes sure to guide you, holding your hand on each topic, repeating theorems already mentioned to refresh your head, not skipping too many steps when solving examples. This feature is seen at it's best in the Series Methods section of the book. Also, the amount of problems is wonderful, they all have solutions and are right next to the problems, unlike the convention, which gives solutions only to the odd number problems and has them written at the very end of the book, something that I hate, for the constant page turning greatly damages the book. Don't you worry, the writer solves many examples and each subject, explaining everything so you can work on the problem set rather easily. The only setbacks that I noticed on this book are that, when teaching the prerequisites to a subject, it doesn't bother to demonstrate the theorems (which is fine by me, because you should already know that stuff in the fist place), and it doesn't have all the fancy graphics that the outrageously expensive ODE books have (for this I use Matlab or Mathematica, so I also don't care about his). You also have to consider that his books is quite old, and the numerical methods are a bit dated, still, any good teacher will fill you in with the little updates made to the subject. All in all this book is nothing short of amazing, I give it all my fingers up to anyone who is taking ODE or wants an awesome reference book. I found it easy to read, precise, and vast. This book will probably do you more justice than anything worth >$100.

This book is awesome, if you're looking for a text on introductory Diff Eq. The start of the book can seem a bit dull, but, as you move through the chapters, it picks up. At the end of each section there are loads of problems, with ANSWERS. This book also has lots of informative pictures to help understand where some of the equations are coming from when explaining a problem. I haven't made it through the whole book yet but so far it's been so worth it's price. Best of luck on your future classes or study journey!

I've become a fan over the Dover books as a quick pickup for math. They are inexpensive, usually pretty solid technically, and understand that you are probably not a mathematician and need your hand held long enough to find your sea legs. You're busy. You need to know this stuff so you can do something else. You're an engineer of some kind with tight deadlines. You're wearing a black belt with brown shoes. You drink way too much coffee and really need to let your kids know you love them more than you do. I know your kind. And it'll be okay. That aside, make sure you have a solid footing on your calculus, because if you didn't do well with calculus, you'll suck with this too. The mistakes just multiply. Again, the authors understand you're not a mathematician, but they know you're not an idiot either and don't need your hand held. If you've got those basic prerequisites (1. Calc 2. Not an idiot) and need to get in the know on DiffEQ, this is a good one.

First, some information about myself. I am a sophomore in college. I took a intro differential equations course last semester. I found it frustrating - the course covered many topics but none quite in depth as I would have liked. I am an engineer, and engineers are not supposed to "care" about the theory, only how to apply it, but I have a certain fascination with differential equations that was definitely not satisfied by the class I took. The textbook we used, Boyce and DiPrima, did not help matters. It was convoluted, spending whole pages trying to explain a concept, chock full of referrals to formulas a few pages back, interspersed with pretty pictures. In short, I appreciated what the authors tried to do, but it did not help me understand differential equations adequately. But alas, I digress. This is not a review of Boyce and DiPrima. Anyway, I began searching around for a book that would let me learn DE's the right way. This book came up in a recommendation, and I decided to try it after reading all the positive reviews about it. I think it does a fine job of living up to its reviews. The material is presented in a very clear, very accesible manner. The book is divided into lessons. Each lesson covers a specific topic. I am currently going through lesson 20, n-th order linear homogeneous ODE's with constant coefficients. The authors give a general overview and discuss briefly that e^mx is a solution to all of these equations provided they have constant coefficients. Then they give the three cases of concern - real distinct roots, real repeated roots, and complex roots. Each of these cases gets its own sublesson, starting off with a generalized equation, a proof, and an example. This isn't so different from what other textbooks do, but something about the uncluttered text, the effort that the authors put into explaining every nontrivial step of a proof, and the organization greatly appeals to me. As icing on the cake, at the end of every lesson is about 40 practice problems...with solutions to every one of them on the following page. Granted the solutions do not have steps, but the material is covered so throughly that a glance back is all you need to solve them. I'll give an example of how thorough the book is compared to Boyce & DiPrima using repeated roots cropping up in characterstic equations of second order homogenous ODE's. Say the root has value m and A and B are constants; the general solution to such an equation is y = Ae^(mx) + Bxe^(mx). In Boyce & DiPrima, the solution is presented in a stupid manner. The authors use an analogy to a first order equation to try and explain why xe^(ax) appears. The fact that I don't even remember the proof is testament to how poorly the topic was explained. In this book, the authors explain that y = Ae^(mx) + Be^(mx) is NOT a solution because the function Ae^(mx) is NOT independent of Be^(mx), and all solutions to n-th order linear homogenous ODE's REQUIRE a solution composed of a basis of n independent functions. Since e^(mx) cannot be used twice, there has to be another function besides e^(mx) that satisfies the differential equation y'' - 2my' + (m^2)y = 0 (of which m is a repeated root). They suggest y = u(x)e^(mx), and substitute this into the aforementioned differential equation. Then it is just a matter of finding u(x). It turns out that u''(x) = 0, so u(x) = B + Cx, Suddenly, it's all clear. The solution is thus y = Ae^(mx) + (B + Cx)e^(mx). But there's more. If the root is repeated 3 times, then the solution becomes y = Ae^(mx) + (B + Cx + Dx^2)e^(mx). And if it's repeated four times...etc. The authors make sure to cover every avenue of curiosity that one might have, in depth. Unlike Boyce & DiPrima, I'll remember that proof for a long time to come. I doubt many other convential DE textbooks present their topics with this much clarity and depth. And that was just one lesson. There are 65 lessons in the 800+ pages of this book. IMHO, the best way to take advantage of this book is to get a notebook, pencil, and paper, sit down at a table, pick a lesson, and go along with every derivation in your notebook. Then do every exercise and check the provided solutions. That's what I'm doing, anyway. It's what makes this book is ideal for self-learners. If you want pictures, go buy an overpriced college textbook. If you want substance and understanding, get this.

I bought this book as a substitute for the assigned textbook in my Differential Equations class. I've done this previously in other classes and have found that most textbooks cover the same material and often in the same order, so it's worth the effort to find one that is written well. In this case the reviews were good and the price was right. The assigned textbook was Boyce and DiPrima, which I had access to from the library. The style of Tenenbaum and Pollard was excellent. Certain sections required reading and rereading, but the section breakdowns are good and the coverage is thorough. I found that by mastering the sections in this book, I was far ahead of what was covered on my exams. The style of the sections is a bit of theory and proof, followed by many examples covering different cases. At the end of each section are exercises and these are followed immediately by solutions, which makes the book very good for self study. A word of warning to those who intend to substitute this book completely for an assigned textbook. The material taught in Differential Equations is largely a collection of techniques and while most books might follow a similar trajectory, one may emphasize certain techniques that another mentions as a footnote. I got burned by not paying attention to exactly which techniques we were covering in B&D and getting tested on things I hadn't even considered, let alone studied. I really enjoyed the coverage of oscillators. The coverage of each case and the notation used has made calculations with oscillators much more intuitive in other classes. The handling in B&D on the other hand was not as good, particularly the notation. As much as I would like to push this as a substitute for B&D, due to the nature of DE courses, at best it can be an extensively used supplement. For those seeking self-study material, I highly recommend it.

I'm not even sure where to begin with describing the awesomeness of this book. This text has to be the absolute definitive source on ODEs for undergrads or beginning grads! And it really should be a model for how all math textbooks should be written. The authors describe everything with patience, clarity, and precision. There are tons of examples in each section and proofs are explained step by step. Then each section ends with a ton of excellent exercises with solutions included on the very next page. The book itself also goes back and forth between pure and applied math by teaching about ODEs for a few chapters and then giving you a few chapters of real world applications of what you just learned. (If you were only interested in the pure math, you could simply skip the application chapters without missing anything crucial. However, I think that skipping the application parts really robs one of understanding the awesome power of the mathematics being learned.) This is an absolutely astounding textbook that has everything you need to self-study the material, and more importantly appreciate the power of the knowledge you are acquiring with the alternating chapters on applications. But I could also see the usefulness in picking up the book simply as a reference or an additional text for an ODE class in which the course's assigned textbook is insufficient. The fact this textbook is less than $20 while dozens of other inferior texts on ODEs are three or four times the price is also quite mindboggling, and only adds to the awesomeness of the book.

There are lots of expensive textbooks on ODE's that are not nearly as clear and complete as this little book. The book is broken down into 65 lessons so that the student's brain does not get overtaxed, since each page is densely packed with essential and clear instruction with lots of examples and exercises with solutions. The book starts with the origin of ordinary differential equations and then moves on to the solution of various orders of ODEs. The author also has lessons on how to solve specific problems using ODE's to hammer home concepts and their usefulness including problems from finance, mechanics, and electric circuits. Since graphical methods and methods involving elementary functions can fail to find a solution to an ODE, the author goes on to discuss methods involving series and also numerical methods of solution. Any supporting mathematical concepts involved in any solution method are also clearly explained, making this very much a self-contained little book. For those more interested in pure mathematics, the last two chapters examine the existence and uniqueness theorem for first order differential equations. Even these more theoretical chapters, though, are tied into the solution of some practical problems in geometry. This book is especially useful for engineers and scientists that are more interested in applying ODE's to solving problems by working lots of exercises accompanied with top-line instruction. With the exception of the last two chapters, mathematical theory is largely presented only to support the explanation of various problem solving techniques. Thus, students of pure mathematics might want to look elsewhere, although there are some proofs included in the exercises. Otherwise this is a nearly perfect book on ODE's and I highly recommend it.

Pretty good book for Diff Eq. I bought this book before I took my Diff Eq class to help introduce me to some ideas and concepts. Mostly, I bought it because it was cheap, and it can be a good reference to explain concepts a little differently than my official text.