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Ordinary Differential Equations (MIT Press)

4.3 out of 5 stars 16 customer reviews
ISBN-13: 978-0262510189
ISBN-10: 0262510189
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Product Details

  • Series: MIT Press
  • Paperback: 290 pages
  • Publisher: The MIT Press (July 15, 1978)
  • Language: English
  • ISBN-10: 0262510189
  • ISBN-13: 978-0262510189
  • Product Dimensions: 5.8 x 0.8 x 9 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #703,036 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Paperback
Be aware there are 2 versions of this book
available in English; this one from MIT press
is (contrary to one of the reviews above) is
translated from the *first* Russian edition;
there is another version from Springer-Verlag
translated from the *third* Russian edition.
They're translated by different people so
some wording etc is different but otherwise
they're similar, though not identical. The
later edition has some reworked passages
and modest amount of new material, but it's
not a hugely different book.
Both are excellent, are are all the other
books & papers I've seen by V.I. Arnol'd.
2 Comments 90 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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Format: Paperback
I had always hated d.e.'s until this book made me see the geometry. And I have only read a few pages.

I never realized before that the existence and uniqueness theorem defines an equivalence relation on the compact manifold, where two points are equivalent iff they lie on the same flow curve. This instantly renders a d.e. visible, and not just some ugly formulas.

He also made me understand for the first time the proof of Reeb's theorem that a compact manifold with a function having only 2 critical points is a sphere. If they are non degenerate at least, the proof is simple. Each critical point has a nbhd looking like a disc. In between, the lack of critical points means there is a one parameter flow from the boundary circle of one disc to the other, i.e. thus the in between stuff is a cylinder.

Hence gluing a disc into each end of a cylinder gives a sphere! It also makes it clear why the sphere may have a non standard differentiable structure, because the diff. structure depends on how you glue in the discs.

What a book. I bought the cheaper older version, thanks to a reviewer here, and I love it. No other book gives me the geometry this forcefully and quickly. Of course I am a mathematician so the vector field and manifold language are familiar to me. But I guess this is a great place for beginners to learn it.

One tiny remark. He does not mind "deceiving you" in the sense of making plausible statements that are actually deep theorems in mathematics to prove. E.g. the fact that in a rectangle it is impossible to join two pairs of opposite corners by continuous curves that do not intersect, is non trivial to prove.
Read more ›
1 Comment 55 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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Format: Paperback
This is one of the few original books in the area of
differential equations. In his clear style, Arnold
presents the basics of differential equations. He is more
interested in understanding the solutions than in deriving
them by analytical methods. The text is well organized and
there seem to be more figures than proofs (although all
proofs are there, it just that they do not get in the
way). A must, if you are in the area of chaos and dynamical
systems. (RM)
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Format: Paperback
It is hardly needed to add words to the existing positive reviews of the book. In the line of previous comments, I just mention that it is an enjoyable book on a basic subject of great interest also for engineers and physicists. The matter is treated with the evident purpose to make the reader fully aware of the interesting geometrical and dynamic implications of the conclusions reached at each step. It is a nice counterexample for those who believe that, to be rigorous, a mathematical book needs to be very hard to read.
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Format: Kindle Edition
This is one of the most beautiful books written on ordinary differential equation and a most read for any interested person.

The ebook format (and all its variants) however does not handle mathematical expressions yet, and formula have to be represented by images. This make the kindle edition unreadable. Add to this the a horrible job done by the publisher in translating it into ebook format.

hopefully, the epub,mobi, ... formats one day will include the mathml extension. Until then, go for the paper edition.
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Format: Kindle Edition
If you consider buying the kindle edition, then just don't! Neither the equations, nor the tables are expandable. You will not be able to read them, even if you wear presbyopic eyeglasses! I bought it and had it refunded within five minutes.
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Format: Paperback
This is a great treatment of DE in an intuitive fashion.
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Format: Paperback
Like his books on classical mechanics, a book that theoretical physicists should read. Unfortunately, the discussion of local integrability is too abstract and there is no distinction made with global integrability. Also irritating: because of a singularity at the origin the damped harmonic oscillator is not recognized as integrable in spite of the existence of a global conservation law, excepting one point in phase space. Integrability is an extremely difficult subject and maybe Arnol'd could have taught us more about it. I've discussed integrability/nonintegrability from a physicist's perspective in my Classical Mechanics (Cambridge, 1997).
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