A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE.
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Most Helpful Customer Reviews
2 of 2 people found the following review helpful:
1.0 out of 5 stars
If you have a class which uses this book, drop it.,
This review is from: Ordinary Differential Equations (Paperback)
I can't believe that this is the fourth edition of this book. Considering the lack of organization and typos, I'd think it was an unpublished draft of a book. It's honestly the worst book I have ever used. I found it harder to learn anything from than rudin. It's unclear what knowledge is a prerequisite for the material here, as the authors seeem to do some sort of review of first order linear differential equations in the beginning but then go off on different tangents. Often terminology will be left undefined, especially in the exercises where it actually matters the most. One highlight of this happening is the chapter on limit cycles, where no formal definition "limit cycle" is actually given. Perhaps this wouldn't be too bad, but there are exercises asking to PROVE things about limit cycles. And I assure you that this is not at all an isolated incident.
My impression is that the authors attempted to write a terse, rigorous account of differential equations. Instead we get an unmotivated disorganized potpourri of topics whose significance is never made clear.
10 of 14 people found the following review helpful:
2.0 out of 5 stars
Full of mistakes,
By
This review is from: Ordinary Differential Equations (Paperback)
This text is based upon lecture notes (written either by Rota and then bound by Birkhoff or vice versa) and it is VERY apparant that the authors spent little time on checking for mistakes. It seems as though every fourth problem has a typographical error or is completely incorrect. This textbook does not take an intuitive approach to the subject and the many errors gives me reason to rate it low.
Nothing is more frustrating to a student than to have a text make a claim, ask you to prove it, and then you find out the claim is false. This is not a unique occurance. Steer clear of this textbook.
3 of 4 people found the following review helpful:
1.0 out of 5 stars
Worst math textbook I have ever had the misfortune of using.,
By Student (USA) - See all my reviews
This review is from: Ordinary Differential Equations (Paperback)
This is a terrible textbook. After being forced to use it for a class, I can safely say that in every set of problems there are at least 5 errors. I'm not talking about small typos--these errors disrupt the entire problem. Often, the author screws up equations entirely in the problems and randomly changes what he has named each variable. Also, it appears as if the authors didn't bother to solve out the problems they were doing. Some of the problems lead to long and tedious computation: if you're in an Ordinary Differential Equations class, you should know how to take a derivative. There's no point in forcing people to solve a fifth order linear Differential Equation leading to a system of 5 equations, it just wastes time and serves no purpose in illuminating the ideas the authors were trying to teach (try taking the fourth derivative of 4 variations of c*e^((sqrt(2)/2)*x)*sin((sqrt(2)/2)*x) and solving for the constants and you'll see what I mean). The book is also painfully outdated (Look forward to computers that can calculate to 7 decimal places!!!) rendering entire sections of the book useless. Half of the formulas are wrong anyway and can't be trusted without verification from someone who is already knowledgeable about the subject. For a book that is so expensive, and in paperback no less, I expected more examples and at least a reasonable editor. Unless you're forced to buy this book, or enjoy reading an unedited copy that the authors clearly didn't even look at after they typed, I would highly recommend against wasting so much of your money. Overall, just a terrible terrible textbook all around and not worth even buying as a reference text.
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