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Physics for Mathematicians, Mechanics I Hardcover – December 6, 2010

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Product Details

  • Hardcover: 749 pages
  • Publisher: Publish or Perish; first edition (December 6, 2010)
  • Language: English
  • ISBN-10: 0914098322
  • ISBN-13: 978-0914098324
  • Product Dimensions: 9.4 x 6.5 x 1.8 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #165,188 in Books (See Top 100 in Books)

Editorial Reviews

About the Author

Michael Spivak is the author of Calculus and the 5 volume work Comprehensive Introduction to Differential Geometry.

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54 of 55 people found the following review helpful By A. Nelson on May 7, 2011
Format: Hardcover Verified Purchase
My review will be mostly comparing the book to Spivak's lecture notes. They are incredibly different.

The first ~430 pages are dedicated to Newtonian mechanics (including central potential, rigid body motion, and fictitious forces). I've noticed most physics textbooks just give this as "God given", but Spivak actually gives some intuition behind what's going on. This book is the perfect foil for Morin's "Introduction to Classical Mechanics".

The discussion of constraints is quite thorough. It begins with rigid body motion, and generalizes it in a beautiful way. Most other physics textbooks leave out any discussion of what to do with constraints (c.f. Arnold's "Mathematical Methods of Classical Mechanics" or even Goldstein).

Spivak discusses variational principles --- not just the principle of stationary action, but others too. Euler's equation derived from variation, Hamilton's principle, Maupertuis' principle of least action, Jacobi's version of the principle of least action, and symmetry in variational calculus. There is a minor typo on page 466 ("Jacobi's form of the principal [sic] of least action.") and it is quite clear that differential geometry is assumed. (Well, Spivak suggests that the first two volumes of "A Comprehensive Introduction to Differential Geometry" should be read before hand.)

There is a thorough discussion of Lagrangian and Hamiltonian mechanics from the differential geometric perspective. It's not completely abstract, it's amazingly grounded in physical intuition. There's an entire chapter (26 pages) dedicated to the Hamilton-Jacobi theory.

The only problem I have with the book is that classical field theory is not covered. Also gauge transformations are mentioned only once in passing. But this book is a wonderful introduction to mechanics for mathematicians, it will save a lot of frustration for mathematical physicists.
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58 of 60 people found the following review helpful By Guilherme on February 26, 2011
Format: Hardcover Verified Purchase
This large book has the same spirit of the author's book A Compreensive Introduction to Differential Geometry. And, as that one, is pretty uncommon. The premises of the book are great: to analyse, besides the advanced mathematical tools avaiable to theoretical Physics (tangent and cotangent bundles, sympletic geometry, etc), the common concepts of elementary Physics with minute details. It is perhaps unnecessary to point out that not many books on Physics do that nowadays. The study of inclined planes is symbolic of the spirit of the book. Spivak explains Archimedes argument, and later gives a complete description of the whole process using rigid body dynamics. The theoretical physicist perhaps never took the pains to do that, but the process should work in some way or another for the whole structure to be consistent. As for the subject, it covers essentially the whole subject of Classical Mechanics, from elementary portions to Lagrange's and Hamilton's equations. The book should interest not only mathematicians, contrary to Spivak's opinion, but theoretical physicists as well, who want to have a well presented and connected account of the mathematical foundations of Mechanics. Is it possible to learn Mechanics from this work? I believe that some portions really could be used for that. Anyway, for someone who already understands Mechanics, is a pleasant fountain of knowledge of the Queen of physical Sciences, Classical Mechanics. And, as usual in Spivak's books, a lot of historical notes illustrate how the subject evolved.

I guess that this is a book which will attract more and more attention as the time passes, and eventually become a classic. Let's just hope that Spivak completes his project of writing Physics books for Mathematicians.
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10 of 10 people found the following review helpful By MzF on September 17, 2013
Format: Hardcover Verified Purchase
I give FIVE STARS to Spivak's "Physics for Mathematicians, Mechanics I" even though I find important things wrong with it. If I could, I'd give this book ten stars because it feels as if it was written for me when it asks many of the same questions I wondered about and tries, mostly successfully, to address them. I knew immediately that I would buy this book when I saw that in the first few pages it addresses the "proof" of the law of lever as presented in Mach's "The Science of Mechanics" and also when Cohen and Whitman's new translation of the Principia is a prominent reference.
This book is a worthy companion to Chandrasekhar's "Newton's Principia for the Common Reader" because it goes into wonderful detail in presenting Newton's approach to (celestial) mechanics. I love the geometric proofs and Spivak goes so far as to take some of Newton's complex diagrams apart and presents them a few steps at a time. Spivak's is both simpler and more detailed than Chandrasekhar, and even avoids the way Chandrasekhar mucks up Newton's clean, precise, and razor sharp proof that the gravitational force within a spherical shell is zero. Chapter 2, on Newton's Analysis of Central forces, is wonderful (even with some of its flaws) and I will be using some of the results in a project I've undertaken concerning the gravitational field of thin disks.

Now for what's wrong with the book. These criticisms arise because of the approach I take as an Electrical Engineer (Control Theory); I'm not a physicist or mathematician.
(1) This book is in dire need of a strong and determined editor; there is almost no consistency in the presentation.
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