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Mathematical Methods of Classical Mechanics (Anglais) Relié – 16 mai 1989

5.0 étoiles sur 5 1 commentaire client

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Book by V I Arnold

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Format: Relié
Ecrit par l'un des plus grands mathématiciens de notre temps, Vladimir Arnol'd, ce livre exceptionnel représente la mécanique classique d'un point de vue géométrique. C'est un « devoir-à-lecture » pour n'importe quel étudiant de troisième cycle ou chercheur travaillant dans le domaine. Les preuves sont merveilleusement claires et concises, les problèmes stimulent de manière rafraîchissante, et les idées sont admirablement intuitives. Achetez ce livre maintenant et vous aurez pour long temps un bon compagnon et professeur !
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Commentaires client les plus utiles sur Amazon.com (beta)

Amazon.com: HASH(0x95541954) étoiles sur 5 20 commentaires
45 internautes sur 50 ont trouvé ce commentaire utile 
HASH(0x955223b4) étoiles sur 5 The best, but challenging for not-mathematicians 21 octobre 2001
Par Francesco Pedulla - Publié sur Amazon.com
Format: Relié
Arnold shines for clarity, completeness and rigour. But, at the same time, he requires a remarkable intellectual effort on the part of the reader (at least a physicist or an engineer). Some readers might see this as a book of math rather than physics, but that would not be fair: Arnold always stresses the geometrical meaning and the physical intuition of what he states or demonstrates. You can take full advantage from the effort of reading this book only if you master a wide range of mathematical topics: essentially differential geometry, ODEs and PDEs and some topology. That's not always true for engineer or physics students at the beginning graduate level. For that kind of readers, Goldstein is a much better fit. Arnold can (and maybe should) be read afterwards.
On the other hand, the exercises, although not very numberous, are very well conceived and help a lot to deepen the comprehension of the text. Also, the order of the topics is linear and very effective from a didactic point of view. The exposition is clear, concise and always goes straight to the point. Thanks to these features, it is one of the most effective books for self-teaching I ever happened to read.
From a physical point of view, the domain of applications is essentially limited to discrete systems. Furthermore, the electromagnetism and relativity are not even cited, although they can be viewed as the logical completion of classical mechanics (see, for example, Goldstein). But the extreme generality of the approach largely balance the more restricted physical domain. In my opinion, the best book you can read on the topics.
18 internautes sur 18 ont trouvé ce commentaire utile 
HASH(0x95522408) étoiles sur 5 Wonderful 26 octobre 2007
Par Nicholas Hoell - Publié sur Amazon.com
Format: Relié Achat vérifié
This book is an excellent introduction to the world of classical physics for NON-PHYSICISTS. While some physicists will no doubt find it accessible, there is considerable reduction of physical concepts in order to get to the heart of the ideas underlying the formalism. Also, the material goes beyond what most physicists (non-theoreticians) will find practical.

He focuses largely on a geometric presentation, in the language of differential geometry, symplectic geometry, differential forms, Riemannian manifolds and includes a large amount of algebraic necessities. This is not a cookbook for learning how to solve classical mechanics, nor is it a math book per se, but it is a wonderful collection of introductions to a vast amount of useful mathematical formalism that permeates the physical literature. I would strongly recommend it to someone needing a thorough supplementary mechanics text, one that relies on very little physical insight and focuses on the geometric and algebraic structures underlying them.

The chapters are very well self-contained for the most part so you can skip to topics you find more appealing without feeling lost. Also, his presentation style is very clever, in case you're a fan of quick thinking and novel presentations (who isn't?).

The prerequisites are familiarity with somewhat advanced calculus and "mathematical maturity". Basic knowledge of group theory would also make it an easier read.
45 internautes sur 51 ont trouvé ce commentaire utile 
HASH(0x955226e4) étoiles sur 5 Encyclopedic 8 mai 2002
Par Professor Joseph L. McCauley - Publié sur Amazon.com
Format: Relié Achat vérifié
Extremely stimulating, uses Galileo to motivate Newton's laws instead of postulating them. Treatment of Bertrand's theorem is beautiful, but contains one error (took me 2 years before I realized where..). However, I know of only one physicist who successully worked out all the missing steps and taught from this book. I know mathematicians who have cursed it. I used/use it for inspiration. The treatment of Liouville's integrability theorem, I found too abstract, found the old version in Whittaker's Analytical Dynamics to be clearer (Arnol'd might laugh sarcastically at this claim!)--for an interesting variation, but more from the standpoint of continuous groups, see the treatment in ch. 16 of my Classical Mechanics (Cambridge, 1997). In my text I do not restrict the discussion of integrability/nonintegrability to Hamiltonian systems but include driven dissipative systems as well. Another strength of Arnol'd: his discussion of caustics, useful for the study of galaxy formation (as I later learned while doing work in cosmology). Also, I learned from Arnol'd that Poisson brackets are not restricted to canonical systems (see also my ch. 15). I guess that every researcher in nonlinear dynamics should study Arnol'd's books, he's the 'alte Hasse' in the field.
30 internautes sur 34 ont trouvé ce commentaire utile 
HASH(0x955225dc) étoiles sur 5 little to say 24 octobre 2000
Par Giuseppe A. Paleologo - Publié sur Amazon.com
Format: Relié
This book is an example of great scientific writing style. Not all the epsilon and deltas are spelled out, and yet the the proofs are nowhere short of rigorous. Besides, they convey insight and intuition: the opposite of Gallavotti's "the element of mechanics" (a very competent book, but obsessed with details). As all the great mathematicians, Arnold separates what's essential from what is not, what is interesting from what is pedantic. It The result is a challenging, wonderful book. I used it (partially) as a second year undergraduate text, and the teacher stressed in the first class that "if you understand Arnold you know classical mechanics". My advice is: get a good grasp of differential geometry and topology and of the tools of the trade (mathematical analysis, ODEs, PDEs) before studying it. Otherwise it will be still readable, but will not be fully appreciated. A last note: it's interesting that Stephen Smale, a mathematician whoshare many interests with V.I.Arnold and is equally illustrious, is another master of style and clarity. You may want to check his book on dynamical systems and his essays.
13 internautes sur 13 ont trouvé ce commentaire utile 
HASH(0x95522c24) étoiles sur 5 A unique, masterful and enjoyable book for graduate student in physics 8 février 2007
Par Peyman Khorsand - Publié sur Amazon.com
Format: Relié
The book is full of little enjoyable details (jewels). Arnold is one of the few mathematicians which approaches problems with a very geometric point of view. In his interview with S.H. Lui he mentions how algebraic picture has dominated the research in mathematics and how he has tried to counter that. One can see the trace of his ingenuity all over this book. What some may call as handwaving in math circles is indeed called as physical (or geometric) intuition in physics community and is being actively encouraged.

The chapters on oscillations (chap. 5) and perturbation theory (chap. 10) are very instructive. For example, parametric resonance is discussed concisely in chapter 5 which you won't be able to find it anywhere else. where can you learn about "Arnold's tongues" better than in Arnold's book?

There are so many appendices at the end of the book. They are often very specialized and I don't recommend you to read them on your first read.

In conclusion, I recommend this book to any physics graduate student. In fact, I hope one day it will be used as a text book for courses in classical mechanics.
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