No comments about Statistical Mechanics of Nonequilibrium Liquids.

No comments about A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics.

4 comments about Symmetry in Mechanics.

1. There are a number of books available on the "geometric" view of physics (Classical Mathematical Physics, by Thirring, The Geometry of Physics, by Frankel, and Foundations of Mechanics, by Abraham & Marsden). The size, level of sophistication and extensive background assumed by these books can be very intimidating. On the other hand, the subject "looks" beautiful, and the benefits of using geometric intuition are desirable to many people.

   Singer's book stands class of its own in these respects. All the basics of the geometrical "machinery" are there, in a book that is only 224 pages in length. Chapter one starts with a standard derivation of the equations of the "two-body planetary motion" problem; subsequent chapters proceed to introduce the necessary modern geometrical and mathematical concepts (differential geometry). The final chapter then revisits the "planetary motion" problem using the modern concepts previously introduced. Excellent!

   There are some misprints, but the author has a Web page of errata. The book has numerous exercises, with many solutions included. I find myself rereading parts of this book over and over.

   Reader be warned; the concepts are new, and it does take work to internalize them. However, this is the most accessible book on the subject available, and also one of the most affordable. The author references many other books, for the reader who wants to go further in the mastery of this subject (one excellent book which is not mentioned, however, is "Differential Forms: A Complement to Vector Calculus", by Weintraub). Enjoy!




2. This is one of the very few books which I returned for refund.
   The subject is intrinsicly interesting, and there is a need for a serious introductory text addressing the subject of geometry and physics. This one badly falls short, - carelessly written, with numerous irrelevant asides. She seems even to fail to realize that there exist three distinct geometric solutions to the Kepler problem. The bound, elliptic case is only one.
   This book has supposedly been written for high-undergraduate students or early-year graduate students. It serves neither adequately.



3. I think the previous review is a bit harsh, and that the book's intents are not what this reviewer expected. I don't think it was the author's intent to write a comprehensive treatise on the subject. The book simply aims at introducing undergraduate students to the use of symmetry in simplifying the analysis of classical mechanic problems, nothing more. If you want a comprehensive treatise, you probably want to read V.I. Arnols's "Mathematical methods in classical mechanics". If what you want is a simple introduction where all the steps are worked out in details, then this book is a good starting point, and I think this is what the author intended. At any rate, the cost ($$$) is quite reasonable.



4. There are two classes of books in mechanics: the extremely physical, which are intended to teach you how to solve problems but lack any mathematical rigour, and the mathematical ones, where the examples are generally one-line statements without any explanation. This book sits exactly in the middle of both: if you are a physicist (or mathematician for that matter) with a fair knowledge of classical mechanics and you understand the basics of Hamiltonian systems, but you want to expand your horizon with momentum maps and symplectic reduction, but you don't understand anything of the hardcore abstract books by mathematicians or you are afraid of them, this is where you should put your money.
   
   Physicists usually simplify their equations by using symmetry in a rather ad hoc way; intuition tells you that a rotation around a certain axis does not change anything or that the system is invariant under translations, or that angular momentum is conserved in a certain direction. Symplectic reduction is the systematic study of these symmetries and how to simplify you equations with them. Don't expect to be shocked because most of the analyses can be carried out without knowing anything about symplectic reduction, but it can aid your life if you are working on more complicated systems, where your intuition does not help you very much (or if you just want to impress someone with your knowledge of mathematical mechanics).
   
   The book does not go deeply into the material, but it explains the basics clearly (symplectic two-form, momentum maps, Lie derivative, reduction...) without being pedantically mathematical. Don't expect any proofs or general theorems; e.g. the author uses (dual) MATRIX Lie groups/algebras, which are intuitive for the physicist (just apply the matrices to your coordinate basis and that's it, quick and dirty) but not as general as the idea of coadjoint orbits of an abstract Lie algebra.
   
   I have tried to go through the mathematics library on symplectic topology and symplectic reduction but have never come very far - and in the cases I thought I understood the concepts I found out that I could do absolutely nothing with it in practice, because I had never seen an actual calculation. After reading this book I must say that I have more confidence reading and understanding them. The book prepares you for more to come, which is exactly what it's aimed at. Instead of giving you the dry reality of modern mathematics wrapped in complete generality, it gives you the juicy extract of what it's all about, it lets you think about it, and use it in simple situations. If you want to go beyond this book, you'll have to have a firm knowledge of Lie groups, Lie algebras, and differential geometry, but for this book, you just need undergraduate physics and mathematics.
   
   The book comes with lots of exercises and to some the answers are given at the back. It's a short and easy introduction to the uses of symmetry (reduction) in Hamiltonian mechanics, and it's good value for your money. I am happy to have it and I can only recommend it.

No comments about Fundamentals of Mathematical Physics (Dover Books on Physics).

No comments about Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups (Advanced Series in Mathematical Physics,Vol 2).

No comments about Phase Transitions and Renormalisation Group (Oxford Graduate Texts).

No comments about Quantum Dissipative Systems (Series in Modern Condensed Matter Physics) (Series in Modern Condensed Matter Physics).

2 comments about Strain Solitons in Solids and How to Construct Them.

1. Professor G Maugin.
   (ASME) Applied Mechanics Reviews,
   Vol.54, No.4, July 2001, pp.B61-B62.



2. Professor Gerard Maugin
   in:
   (ASME) Applied
   Mechanics Reviews,
   Vol.54, No.4, July 2001, pp.B61-B62.

No comments about Geometric Algebra and Applications to Physics.

4 comments about Mathematical Analysis of Physical Problems.

1. This book is much different than the other books dealing with math and physics. A brief description for this book is represent the link between the math used to describe the physical phenomena and the physical phenomena itself, in other words is the answer for this question why this mathematics exactly used in this particular phenomena? which a lot of physics mathematics books don't viewing this point. It is unique and great book.



2. This is a very good feeling, when you handle a book which provides all the mathematics (separation of variables, Fourier Laplace analysis, complex plane integration, Green's functions...) necessary to solve almost all the physical problems; especially dealing with partial derivative equations (from vibrating string to Schroedinger equation). The price is also a good point. Thank you Dover.



3. Well this is a good Mathematical Reference Books for Theoretical Physisicst but has nothing to do with Mathematical Analysis of Physical Problems. It has all the tools you need that is fine, there are many similiar books as a reference book but if you think you will find ideas and methods "how to structure the Physical Problems in Mathematical terms", this is not the book.



4. I have a graduate physics degree (as well as an undergrad math,physics dual major deal..) What I was looking for (and having a hard time finding) - was a book that explained HOW certain equations came about. For e.g. - we all know the equation of a vibrating string or of an electron in a potential well - but if you were the FIRST person to try and discover the equation - how would you go about formulating it? In other words - what would be your 'mathematical analysis' of the 'physical problem' of the vibrating string etc?
   While this book does not go the whole 9 yards in this regard - it is one of the few books (in my limited experience) that actually DOES attempt to 'derive' these equations from scratch! For that reason - I give it 5 stars.