5 comments about Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics).

1. 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.



2. Best book on CM (based most on symplectic formulation). Extremely clear if one has enough patience to follow exactly the author's way and to work out the proposed stimulating problems. Contains an original way of introducing differential forms, integration of differential forms and homology/De Rahm's thm.: you fully get in the subject in few pages ! The first part does not make use of symplectic formalism but is also quite original and stimulating. The level is last yr. undergr. 1st yr. graduate. Very useful if used with E. ott (Chaos in Dynamical Systems) for studying nonlinear dynamics.



3. I have to admit that I haven't thoroughly read through this text. But judging from the first 10 pages, there is a lot of mathematical handwaving. In contrast, foundations of mechanics (hereafter FOM) is far superior in that it provides all the necessary background beyond calculus and linear algebra to the reader, and is logically consistent so far in my reading. I want to mention that there are certainly complete and excellent texts out there on functional analysis, differential geometry, and topology, but many texts include way more stuff than you would want to know. In particular, it is my humble opinion that once you get to a certain point of knowledgeability of a subject like algebraic topology, you have enough of a taste for it that to learn more of the subject would only help if you were to go into research. Therefore a book like FOM provides a concise and practical treatment of those various advanced mathematics topics.



4. 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.



5. 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.

5 comments about Fundamentals of Statistical Processing, Volume I: Estimation Theory (Prentice Hall Signal Processing Series).

1. This is one of the best references on statistical signal processing. The topic is not of simple matter, but the author presents the materials clearly together with great examples. The book is reader-friendly and is relatively error-free. I have bought several copies for my PhD students at Georgia Tech.



2. This text is very good for those who start doing research in statistical signal processing. A lot of explanations, technical terms are well presented and consistent, plus a number of examples that help you to learn about different statistical signal processing concepts and algorithms. Research students can be beneficial alot from this text.



3. I've had tough courses on statistical signal processing as a post-grade student. I am often confused in front of a problem and turning back to the notes taken in class doesn't help much.
   When you read this book all gets bright. I am still wondering how some teachers can be so confusing while such good books do exist...
   However don't count on it for in depth mathematical demonstrations, it starts with a practical problem and explains how to model things. Thus it is a bit bottom-up but anyway starting from a good graduate level in signal and stats.
   I got this one at the library but already ordered a copy for myself and am planning to get part2 on detection.



4. Without any hesitation, I consider this book as a masterpiece in the area of statistical signal processing. Kay takes the reader to the journey of estimation theory as if a science teacher takes his students to a field trip. The one special feature of this book is the convergence of thought that reader obtains upon reading the book. Kay lays a fundamental bridge between various estimators using his succinct style for describing the subject.

   Few special areas require more attention in this book. For example the coverage of EM methods is very condense and requires more elaboration. Also there is no discussion on the estimation methods using higher order statistics.

   Overall I consider this book as the best book I have read ever and I highly recommend this book to those who want to obtain an ever-lasting view on statistical signal processing.




5. One of the best written textbooks I have ever read, in any field. Crystal clear, and is a gold mine of knowledge.

5 comments about The Variational Principles of Mechanics (Dover Books on Physics and Chemistry).

1. .
   This was probably a good book in its day (1950-1970), but
   it's really old-fashioned now. A lot has happened in the
   field of mechanics since Lanczos wrote it. For example:

   - Computers are now used extensively to analyze and
   simulate mechanical systems.

   - The modern language of mechanics is much more geometric
   and independent of any particular choice of coordinates.
   If readers stop at Lanczos, they will have trouble
   understanding the modern literature. He doesn't even
   distinguish between vectors and one forms.

   - Dynamical systems theory / qualitative dynamics has
   contributed a lot to the understanding of mechanics
   in the past 30 years. You won't read anything about
   stable/unstable manifolds or strange attractors in
   Lanczos.

   The "problems" are so easy that they border on the
   ridiculous. And don't try finding them at the end
   of each chapter --- this book predates modern textbook
   format. Lanczos hides his problems like Easter eggs.

   In conclusion, this book is of historical interest only.
   If you want to learn about modern mechanics, read
   something that was published recently.

   (I should add that the book is well-written, but that
   doesn't fix the fact that it is dated.)




2. Lanczos makes mechanics feels like art in this superb work. Analytical Mechanics is the foundation of physics and Lanczos has complete command of the theme. The purpose of this book is to make one understand mechanics "from inside" and not to stress methods of problem solving. Lanczos says that very clearly in the preface. The beauty of the book is that it's not in the same category as Goldstein, instead feelink more likely to Landau, so the bad criticism of the 2-star guy comes from someone that missed this.



3. From organization, to prose, to content, to price, this is the best book on the Hamiltonian and Lagrangian formulation of Classical Mechanics. I just wish this book treated more subjects! The numbered list organization with pithy summaries really works for me. The thought provoking and mathematically fluent prose style is a joy to experience. The author is clearly a master of Einsteinian Relativity, Classical Physics, Differential Geometry, and function analysis. In fact I seem to recall him writing some other books along those lines. Lanczos is a real treat to read. I have read parts of over a dozen different books on Intermediate/Advanced Classical Mechanics and the things the Lanczos covers are just supperb. As a standalone text, it may not be the best choice, but when accompanied by Arya or Hand and Finch it is very enriching. FLuent and cohesive are the words that come to mind when describing this work. This book is especially good for someone who knows a good deal of math and would like to be introduced to classical mathematical physics.
   
   I heartily recommend Lanczos's masterpiece!



4. If you ask 10 PhD scientists: "Why is Schrodinger's Equation complex?" (contains the square-root of minus one), 9 out of 10 won't be able to give you the correct answer.
   
   It has little to do with taking the root of negative numbers. After reading Lanczos you will know it has do with "space" and what is a proper physical law. (Now you have to read the book to parse this sentence. Good.)
   
   This is one of many wonderful insights Lanczos provides; with humor, wonder and crystal clarity. This is not a 'text book' on mechanics, you will get more out of it if you are familiar with the subject. He gives you understanding, not technique.
   
   It is as if you can hum a few tunes. Reading Lanczos is experiencing the entire opera for the first time. Now you know the full story, how each aria is a part of the fabric; how each fits in the situation, the motivation behind it. The tunes you liked become richer, more profound, they are connected. The next time you sing you fancy you are a Caruso, a Puccini.
   
   It is so rare to encounter a master who is also a gifted writer.
   
   Some reviewers compare Lanczos to Feynman's Lectures, I agree partly. Lanczos is more literate and much more humble. Feynman is so busy being the genius from Brooklyn that his exposition is choppy and uneven. Lanczos is a better organizer and writer.



5. I've read this gem and done most of the evercises in about 3 months. Before that legendary book I'd had the usual crappy course in Classical Mechanics based on Goldstein. The bottom line is the book will show you a lot of advanced material and unfamiliar manipulations. On the other hand there are sometimes statements lacking proof or more detailed lucid explanation. The book is appropriate for readers that already know what action is, totall beginners will be too shocked by the new concepts and won't be able to pick up the important nuances revealed by Lanczos.
   
   Lanczos work clarified some of the concepts in which my CM course failed:
   - the important difference in treating holonomic and nonholonomic constraints
   - exact constraints are mathematical idealization of infinitely rigid constraint forces
   - Lagrange multipliers for functionals (actions) not only functions
   - the logical thread virtual work -> d'Alembert -> Hamilton's principle
   - the connection between the action in configuration space and in phase space
   
   The book introduced me to topics not covered by the course, which was my initial goal:
   - elimination of ignorable variables in L or H formulation
   - canonical transformations, definition and importance
   - generating function of canonical transformation
   - test for canonicity of transformation using Poisson brackets
   - integral invariants of canonical transformations
   - Hamilton's principal function
   - Hamilton-Jackobi equation and analogy with optical wave surfaces
   - separation of variables in H-J equation
   - action-angle variables for separable periodic systems
   - evolution of the system as a sequence of canonical transformation
   - introducing geometry and geodesics in phase space
   
   The reading definitely increased my freedom in manipulating the variational problem into equivalent variational problem. Examples of the two most weird for me manipulations are in the appendices. In the first appendix the Hamiltonian formulation is derived from the Lagrangian by introducing new variables, constraints and corresponding Lagrange multipliers, and then eliminating the variables. In appendix II, the most popular cases of Noether's theorem are derived by introducing new field variables in the action - I had no idea that was allowed. Very interesting was the idea that the world line of the system in configuration space can be parametrized with arbitrary parameter and the time becomes a function of that parameter that is varied together with the other generalized coordinates. Such variation is normal for GR but I've never seen it done in non-relativistic mechanics.
   
   Some of the other reviews described the book as 'lucid'. I find that eggagerated - although the book shows lots of unfamiliar manipulations, sometimes proofs of validity or the necessary more detailed conceptual or calculational explanations are lacking. An example is the inclusion, all of a sudden, of the time as variable to be varied - where is the proof one is allowed to do that? In another case, the book tells you that by nullifying the boundary term when varying the action, one gets 'natural' boundary conditions for the Euler-Lagrange diff. equations. I failed to see how the physics of the problem would demand exactly those boundary conditions. Where the analogy between mechanics and optics was discussed, the book creates the impression it derived the Fermat's principle but in reality it simply proved that the path following the gradient of of constant surfaces is shortest between two points. So there is a certain gegree of fuzziness on calculational level (lacking proofs of validity) or conceptual level (underexplained concepts and relations).
   
   I liked the the abundance of historical notes. You will learn that there are several formulations of the least action principle - Euler and Lagrange version, Jackobi version and Hamilton version. Each subsection has a small summary and there are a few problems per section to illustrate the main ideas but not enough for exercises.
   
   There are two chapters that I think appeared in later editions and are too sketchy compared to the book core:
   
   Chapter 9 discusses special relativity where you can see that guessing the relativistic Lagrangian on general grounds of Lorentz invariance gives almost effortlessly the relativistic dynamics without the usual gedanken experiments. At the end, Lanczos dives a little into GR using the Schwartzchild metric to derive orbits, bending of light rays and gravitational redshift around spherical body.
   
   Chapter 11 gives a short presentation of fluid mechanics (a little unclear derivation, in Lagrange and Euler coordinates), elasticity, and electromagnetism. Noether's principle is used to derive the canonical and the symmetric energy momentum tensor. I haven't seen a crystal clear derivation of Noether anywhere and Lancsoz is not an exception. The problem is as usual ommiting what exactly is being transformed and why is that allowed.

3 comments about Elements of Gas Dynamics.

1. The book arrived quickly and I found the book the way it was described



2. This book is really good. However, I don't recommend it for an undergraduate level student. Equations are sometimes proven by saying, "after some manipulation." As a reference or a graduate text however, this book is very nice to have around. It is small and the chapters are well labeled.



3. I used this book during an undergraduate research project in the UK in 1971 on gas discharge from a resonance tube and found it provided the heart and soul of the topic. While slightly challenging for a senior undergraduate student it inspires motivation to persevere with the theoretical foundations and analytical techniques leading to full enrichment in understanding the topic. Even though my graduate degrees focussed on space robotic dynamics and control I still fervently revere Liepman and Roshko's book as a lifetime refernce companion on gas dynamics.

5 comments about Quantum Mechanics: Non-Relativistic Theory, Volume 3, Third Edition (Quantum Mechanics) (Quantum Mechanics).

1. There are no words to express the amazing clarity of this book. I came across it at the library. I only have a passing interest in science but, despite the high level at which this book was written, this book helped me understand that there are things in this world called electrons that don't have a velocity or a path in the classical sense. When I die, I'll be one of the few that truly understood this amazing physics of our world thanks to this book. I cannot understand the whole book, but that is not the fault of the book. It is written for very specialized individuals thinking on a very high level. Some examples are included, but I suspect they are unnecessary as the exposition is superb. It is truly a work of art.



2. It is really a shame to have such a classic text with a typesetting that makes much of the mathematics almost unreadable. For example, the authors often use either a tilde, hat (carat), and dot (period) on top of operators, sometimes in combination. These are so badly rendered that you have to derive their identities from the context of the surrounding discussion. Frequently parts of characters are missing as if an old typewriter with a worn ribbon were used. I have 2 other volumes in this series (Mechanics and Statistical Physics Part 1) which do not suffer these defects. My 2-star rating is in no way a reflection of the contents nor the authors, which get 5 stars (based on the prose and the equations I CAN read).



3. this is very great theoretical quantum book. Although you cannot start learning quantum mechanics from this book, But for extended theoretical studies, in the concept of quantum mechanics in general, and also in specific fields. I recommend this book. This book is number 5 of my quantum books, it is so far the most consistent, but I understand also this is because quantum is not a strange subject to me any more. I really recommended for graduate students, or undergraduates who have good understanding of the mathematical calculation for basic quantum.
   great book after all.



4. Great supplement to Griffith's book as well as Woodgate's book. Some of the other positive comments here say it all.



5. If one wants to understand Quantum Mechanics then she or he should read this book.

5 comments about Quantum Mechanics Demystified.

1. Alright...first of all. NO there is not too much math in this book. Quantum Mechanics is basically all math. Books that don't use math are usually worthless if you want to learn QM.
   
   BUTTTTT....i reccomend everyoen go buy this book to have as a ref. It has quite a few typos..Dont worry, you'll catch them (they're retarded)..But more importantly, the author explains things much better than alot of Quantum books do...
   
   Get it but be weary of the math. You'll see the errors when you start working the problems.
   
   -Brit



2. This is a good book for anyone trying to teach yourself quantum mechanics, and it is a good supplement to any quantum mechanics class. The author talked about hopefully making a 2nd book on this topic to add to this book (not a 2nd edition, but another book) because this one does lack some of the more complicated topics in quantum mechanics.



3. This book might be a decent supplement for more rigorous introductory texts such as Griffiths if it wasn't for the unbelievable number of careless errors and typos. Almost every page (no exaggeration) has at least one error. While most of the errors are self-evident and easily corrected, some do lead to confusion and frustration and all produce in the reader a general mistrust of the text. It is amazing that a reputable publisher like McGraw-Hill could have let a book this mistake-ridden go to print. Errors aside, the content is not self-contained and is not suitable for self-learning, as there is little explanation of the physical meaning of the math and almost no rigorous development of the theories. There are plenty of instances where concepts are used that have not yet been explained, such as the definition of the square of the absolute value of the wave function and the Hamiltonian operator. It
   might, however, serve as a supplement for other introductory texts, since it offers simple problems that help reinforce calculation techniques, which tend to be lacking in texts such as Griffiths which contain more meaningful but more difficult problems. Regardless of its merits, a revised, corrected edition is needed.



4. I went through this book twice and found it very helpful in getting a basic familiarity with elementary quantum mechanics. Its strong point is the detailed exposition of the calculations which enables even people without a lot of math background to master and understand the material. The main problem is innumerable typos, which paradoxically are a kind of learning experience because they force you to go through each calculation in detail to correct the mistakes. But really, it's a shame that so little effort was made at proofreading before the book was published. The reader deserves better.



5. This book is completely useless. It describes itself as basic enough for beginners yet complex enough for advanced students. I would consider myself somewhere in between this, but didn't find either of these claims to be valid.
   
   Equations are introduced with no context what-so-ever. I expected something that would be a gentle enough (re-)introduction to the subject. No, it's just straight in there with no explanation of anything. On the cover there is a nice cartoon of Schrodinger and his cat - which suggests the tone of book. Unfortunately, this is misleading (I know: books, covers, judging etc) - the cat never appears. Schrodingers equation appears - but I had to go elsewhere to find out its origins.
   
   I can't suggest an alternative - but stay away from this one.

4 comments about Schaum's Outline of Statics and Strength of Materials (Schaum's).

1. Plese send for me about the screw test in all universities. Tank's all over.



2. This book is full of mistakes. I spend more time checking the author's work that I do practicing. Don't waste your money or time with this.



3. I have found it helpful in confirming information I was not sure about.



4. This book is a great self teacher of statics and beam mechanics. It has the best treatment of the "singularity function" method for beam loading that I have read.

No comments about Fundamentals of Fluid Mechanics, 5th Edition, JustAsk! Set.

No comments about Schaum's Outline of Fluid Mechanics (Schaum's Outlines).

4 comments about Newtonian Mechanics (M.I.T. Introductory Physics Series).

1. I think it's THE book of mechanics for Physics' students. Itcovers from basic mechanics (kinematics, newton laws...) to sometopics of classical mechanics. It has many clear demonstrations that are not found in other books for engineers (like Resnick, Tippler...) and contains excellent examples. It has a high level but is very easy to understand. French style, that combines history, original observations, clearity and high-level topics makes you love Mechanics.



2. I worked through French's challenging problem sets in Newtonian Mechanics while I was in the military and found out that I could "do physics." I immediately returned to school to earn my physics degree. A lot of authors mention in their prefaces that the best way to learn physics is to do problems. I agree. Reading the text of this book is easy for anyone who desires enough to do it. Working the problems (always the tougher and less convenient half) will pay dividends in confidence and deeper understanding. This book--like the rest in the MIT physics series written by French--has all of the answers to the problems in the back of the book that allows independent study. The book is well-motivated and gives a lot in return but asks a lot of the student in his or her maturity and perseverence.



3. This is an excellent text, especially its challenging problems and also the wonderful explanation of historical contexts. This 1st edition (743 pages) was published in 1971 and is the most appropriate one to use for a more leisurely course that covers both mechanics and some history of mechanics. Definitely less daunting than "An Introduction to Mechanics," by Kleppner and Kolenkow, 1973 - which has more difficult problems.

   The 2nd edition (310 pages) was published in 1986 and was renamed "Introduction to Classical Mechanics," by A.P. French and M.G. Ebison, Kluwer Academic Publishers. This latter updated edition is much more compact and drastically removes most of the historical and discursive material. More emphasis is placed on rapidly developing the principles and applications, thereby achieving the same depth but reducing the number of pages by more than half; unfortunately, it's also much more expensive - characteristic of Kluwer books. It seems to be more often used in British universities.




4. This review and rating refers to the physical quality of the book, not to the content quality. It seems the book currently published by Norton is a poor quality photocopied version of the book. The diagrams with the grey backgrounds are really bad. I understand that the technology that was used to originally publish the book is obsolete but that does not excuse the current poor quality reproductions.
   
   Although Norton is the only publisher of this title, the other titles in the series are also available from another publisher although I cannot confirm if the print quality is any better.