2 comments about Linear Functional Analysis (Springer Undergraduate Mathematics Series).

1. This undergrad text is extremely clear, with lots of examples and exercises. I thought the coverage was a bit limited, even for an undergrad text and the writing style is kind of dry. Still, it's perhaps even easier than Kreyszig.



2. I highly recommend this book for independent study or as a supplement to a text. You can see if you're on the right track with exercises because the text has solutions and hints in the back. People must keep in mind that this book focuses on linear functional analysis and not functional analysis in general.

4 comments about Introduction to Tensor Calculus and Continuum Mechanics.

1. Why is it that no one else has reviewed this book? It stands out totally, in every respect, as a carefully developed teaching manual that both challenges, stimulates and gently leads one on into a rarified esoteric world, by a master of the subject.
   The combination of his expertise in the subject matter and his teaching experience has produced a powerful aid to the understanding of tensor calculus and its many applications, to benefit students the world over (many of whom were attracted by his free download of 80% of the final text, for which...thankyou!)



2. I don't have much to add to the previous reviewer, but given the astonishing lack of reviews of the book, let me give a second datapoint for those who are considering buying this book.
   
   This book is the most gentle introduction to tensor analysis I've ever seen. It was obviously written by someone who puts a lot of thought into teaching. The book is certainly within reach to advanced undergraduates, and would also be appropriate to beginning graduate students.
   
   Aside from a stellar presentation of the subject, the exercises at the end of the section are marvelous. In fact, I would consider the end-of-section problems to be another one of the book's strengths.
   
   The one thing that this book may lack is the "modern" approach to tensors -- the book definitely focuses on the classic "a tensor is a set of numbers or functions that transform as a tensor" approach. But I don't consider this a weakness. The classic approach is easier to learn, and certainly more accessible. The modern approach to tensor analysis can always be picked up later, but in the meantime, this book makes what could be a very abstract subject very real and tangible.
   
   If you want to learn tensor analysis, or are considering the book to teach from, do yourself a favor and get this book. It's hard to fathom anyone being disappointed by it.
   
   Hmm. I guess I did have some more to add to the previous review. :)



3. I basically have bought at least half of the tensor books out there; J.H.'s book set me on the right path. Most books open with mind boggling notation juggling acts without the purpose set forth. Its clear here that you are taking vector notation and converting it to indicial notation for calculus and vector stuff like div, grad and curl and various combos of vector formulas. The examples are great! I am Mathcad user and am used to just plugging in numerical data using plain old vector notation, so learning indicial notation is something new.



4. I still find some of the material in this book very hard to follow. However the majority of the material is really well presented and very helpful.

1 comments about Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations (Cambridge Texts in Applied Mathematics).

1. Good book. I'm mostly interested in evaporation/condensation phenomena in a gas, the book provides review of history of development of the field (with references), and also provides comprehensive analysis with derivations.

5 comments about Quantum Mechanics, Vol. 2.

1. Almost no words needs to be said about this masterwork.
   And rare are serious students of quantum mechanics who could really afford to ignore it.
   Several important techniques and recent developments are omitted, but having grasped the material presented in these two volumes, learning further about quantum mechanics will prove astonishingly straightforward.
   A caution remark is in order, though : these books don't really suit to self-study, due to their sometimes rather lengthy, verbose exposition, which could well quickly fade away an initially strong motivation for studying quantum mechanics, if not bolstered by a teacher's or fellow student's incentives.



2. If you're looking for a one-stop reference for your physics library, this is it. Complements ANY textbook, in fact it stands on its own better than any other quantum mechanics textbook that I've used so far (Including Sakurai, Bransden-Joachain, Gasiorowizc, Griffiths). The notation is convenient and easy, worked out "compliments" show you how to apply concepts and build your problem solving skills. Even as just a casual read on subjects you may not have been exposed to yet/ever, this text is great. I had this text recommended to me by basically every grad student and professor I've talked to, and I can now recommend it myself.
   
   That said, many complaints I've read here have a common thread. This is not meant (at least it shouldn't be meant) as an undergraduate text. It definitely assumes at least a moderate understanding of underlying principles, although you don't have to be a genius either. I would never recommend this to an undergraduate student until you have been exposed to at least 2 semesters of the introductory stuff. Period.
   
   Buy this book if you're looking for a one-stop quantum mechanics reference, for your graduate studies.



3. The service was very good and swift. The book was in excellent condition. Thank you.



4. I chose not to rate this product It was received in like used condition even though it was wrapped in plastic. it was litterally crammed into packaging that was barely big enough to hold it. that packaging was simple a brown envelope when I received the book there were some gouges in the packaging and the book had gouges in the edges of it that extended into the chapters of the book itself.
   
   I am very dissatisfied with this product and will avoid amazon in the future.



5. I was disappointed with the packaging they sent the book in. It was only wrapped in paper on two ends, and the paper had ripped open so the book was barely in its package by the time it showed up in my mailbox. Somehow, the book was still in decent shape despite its packaging.
   
   The book itself is highly technical, not a very easy read, but very thorough in dealing with the many facets of quantum mechanics.

3 comments about Mathematical Methods: for Students of Physics and Related Fields (Lecture Notes in Physics).

1. When I took undergraduate quantum mechanics 30 years ago, we learned a lot about Louis deBroglie, Max Planck, the photoelectric effect, then moved into wave functions, the Schroedinger equation, simple one-dimensional potentials and the hydrogen atom. Maybe there was a little angular momentum tossed in. It was not until graduate school that I learned much about

   /X> = xi/x>

   where /X> is a vector in an n-dimensional, linearly independent vector space and the xi's were its components in the basis /x>. A lot of things like representations might have made more sense. Anyway, Hassani's undergraduate text gives one an excellent view of vectors and coordinate systems. In particular, it trains one well to leap into the more abstract view of vectors one reads about in, say, R. Shankar's excellent book on quantum mechanics, and also gives one a good deal of exercise on how to translate between coordinate systems. In graduate school, I found the ability to roam between coordinate systems to be very, very handy and the laborious time spent learning it was worth it. I'm not done with this book yet. I'm now getting into his chapters on complex variables and differential equations, but Hassani's treatment of vectors and coordinate systems is very good indeed. Undergraduate physics students who plan to go on into graduate school will find time with this book well spent.




2. This book is for those who already aquired some knowledge in mathematical analysis, linear algebra with vectors and some introduction in complex analysis. Roughly altogether about 15 University points.

   Because it's surely not teaching you key things like what limits, substitution, integrand (one page according to index), asymptotics and so on really are. That knowledge is expected of you to have.

   Instead the book gives a sort of enhanced recapitulation and expansion on topics and new insights on new topics as well; what these can be used for and how to use them. This is great because the reading goes intellectually much faster and get your attention right away with the stuff you already have a working knowledge of.

   The boxes are great; containing important definitions which then is accompanied with instant examples clearifying the definitions by proof or otherwise gives descriptive and explanatory content for a method or definition

   Hassani's book is also well written in terms of language use.




3. Helps students become familiar with complex mathematics in more applications than a standard course. Not as thorough as the books covering the same material by Mary Boas. IMHO.

5 comments about Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics).

1. This is a very useful book for understanding modern physics. You absolutely need such a book to really understand general relativity, string theory etc. For instance, Wald's book on general relativity will make much more sense once you go through Nakahara's book. It is very complete, clearly written, comprehensive and easy to read. I would also recommend Morita's "Geometry of differential forms' and Dubrovin,Novikov and Fomeko's 3 volume monograph, if you can find it. All in all, Nakahara's book is one of the best buys, precious book.



2. No doubt, the interplay of topology and physics has stimulated phenomenal research and breakthroughs in mathematics and physics alike.
   
   Unfortunately, there is so much mathematics to master that the average graduate physics student is left bewildered.....until now.
   
   The text is an excellent reference book. I emphasize reference. The book presupposes an acquaintance with basic undergraduate mathematics including linear algebra and vector analysis.
   
   The author covers a wide range of topics from tensor analysis on manifolds to topology, fundamental groups, complex manifolds, differential geometry, fibre bundles etc.
   
   The exposition in necessarily brief but the main theorems and IDEAS of each topic are presented with specific applications to physics. For example the use of differential geometry in general relativity and the use of principal bundles in gauge theories, etc.
   
   Unfortunately, there are very few exercises necessitating the use of supplementary texts. However, to the author's credit appropriate supplementary texts are provided. The author goes to great lengths to show which texts inspired the chapters and follows the same line of presentation.
   
   Perhaps the greatest attribute of the text is to take disparate branches of mathematics and coallate them under one text with applications to physics. In doing so one gains a better grasp of how the fields of mathematics interact in the domain of physics.



3. This is the best book of its type, that is, a book that contains almost all if not all the advance mathematics a theoretical physicist should know. I have studied chapters 2-9 and it has the perfect balance between rigorous presentation of topics and practical uses with examples. The level is for advance graduate students. The range of topics covered is wide including Topology topics like Homotopy, Homology, Cohomology theory and others like Manifolds, Riemannian Geometry, Complex Manifolds, Fibre Bundles and Characteristics Classes. I believe this book gives you a solid base in the modern mathematics that are being used among the physicists and mathematicians that you certainly may need to know and from where you will be in a position to further extent (if you wish) into more technical advanced mathematical books on specific topics, also it is self contained and brings lots of exercises that help learn the concepts presented, my advice, get it is a superb book!



4. This book provide a complete and useful review of geometrical instuments of mathematical physics from the beginnig to the most advanced topics of interest. It can be used by students at the beginnig of thei studies in this topics, and it's found to be a useful gallery for higher level students (or scholar).



5. Reading all the glowing reviews of this book, I wonder whether the reviewers actually tried to use the book to understand the material, or just checked the table of contents. There are so many misprints, throughout, that one wonders if the book was proofread at all. Some of the mistakes will be obvious to every physicist - for example, one of the Maxwell equations on page 56 is wrong - others are subtle, and will confuse the reader. The careful reader, who wants to really understand the material and tries to fill in the details of some of the derivations, will waste a lot of time trying to derive results that have misprints from intermediate steps which have different misprints! Some chapters are worse than others, but the average density of misprints seems to be more than one per page.
   The book might be useful as a list of topics and a "road map" to the literature prior to 2003, but that hardly justifies the cost (or the paper) of a whole book.

2 comments about Scientific Computing with MATLAB and Octave (Texts in Computational Science and Engineering).

1. As you would expect from Springer, here is a technically very accurate book. It goes over the main concepts of numerical analysis, which the authors call "scientific computing". Same thing, really. Unlike earlier years, where someone studying this field would have to write out her own Fortran code to apply the methods, we now have MATLAB. The authors chose this powerful package as one in which to explain and implement the algorithms.
   
   These algorithms are essentially unchanged from what a book on the topic might have described, 20 years ago. Finding numerical integrals, roots of equations, solving linear systems of equations etc.
   
   But using MATLAB helps streamline any coding. And you are encouraged to code, in the problems supplied by the book. There are even answers to some of these. So quite apart from understanding the concepts, a bonus is that you can become quite adept at fully using MATLAB's abilities as a research tool.



2. This is an el-cheapo British attempt to teach Matlab to scieneers, inapropriate for American readers.

5 comments about Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis (Methods of Modern Mathematical Physics).

1. We used this book in Math 401 at Princeton. This book is great, well-written, well-problemed. It is curious that the other reviewer complains that there is nothing original in this book, because this subject is older than the author, who is an expert in Schrodinger operators. The parts of the next three volumes which I have read have also been great.



2. This superb book may be the best available text on elementary general topology, functional analysis and spectral theory of bounded normal operators on Hilbert spaces. The exercises are excellent as well. Must reading!



3. Books on mathematical methods "for physicists" are often criticized by their superficiality, a sacrifice deemed necessary for achieving completeness. This one is a glaring exception: the first of a set of 4 (!) volumes dealing with the finest tools for dealing with the delicate mathematical questions in quantum theory - namely, functional analysis. Of course, this sounds rather vague, since quantum physics makes use of functional-analytic tools as diverse as distributions, Hilbert, Banach and locally convex spaces, spectral theory, semigroup theory, operator algebras, etc.
   
   However, do not expect ready-brew formulae and cookbook recipes: this book gets his job done at least as well as Rudin, Yosida and Riesz-Sz.Nagy, just to mention the classics. Most theorems are rigorously proved, and although the book becomes more and more biased towards mathematical physics (i.e., methods for proving self-adjointness, analysis of spectra and scattering theory, as stated in the section "Three Mathematical Problems in Quantum Mechanics". These methods occupy most of the three remaining volumes) as it proceeds - this bias becomes the true reason of being for the last two volumes - this particular volume has precisely the most useful stuff: metric, Banach, topological, locally convex, and Hilbert spaces, bounded and unbounded operators. A supplement extracted from the second volume with the basics of Fourier transforms makes it self-contained as a monograph.
   
   However, the best things, that make this book nearly unbeatable, are the several wisely chosen examples and counterexamples, the notes at the end of each chapter and the wonderful - and useful - exercises. Many working mathematicians I know use this book seriously in their research and their courses in Functional Analysis - a fact that cannot be underestimated and will hardly be equaled by any book on mathematical physics.
   
   If you work on (axiomatic) quantum field theory you may also want to keep an eye on the second volume of the set, "Fourier Analysis, Self-adjointness", which is a bit more specialized but just as wonderful.



4. Fast delivery, newer edition than what was advertised but that's perfectly fine with me



5. This is the best functional analysis book for beginners, in my opinion. It is written for people that are interested in functional analysis as a tool for differential equations. What makes it different from other books on this subject are the numerous examples and applications to differential equations. Highly recommended.

1 comments about Special Relativity (Springer Undergraduate Mathematics Series).

1. This book requires only a working knowledge of linear algebra and multivariate calculus, and a basic understanding of classical mechanics and electromagnetism.
   
   The author begins by providing a simple but general mathematical exposition of relative motion in classical mechanics. The next two chapters review Maxwell's equations and what they imply for the propagation of light. Having set the stage in this way, the axioms of Einstein's theory are introduced and their implications worked out mathematically, leading the reader to a clear understanding of Minkowski four-dimensional space time and the Lorentz transformation. The exposition is accompanied by a number of classic brainteasers in special relativity.
   
   The weak spot (and hence only four stars) is the treatment of the mass-energy equivalence, which does not include a rigorous derivation of Einstein's famous formula E=mc^2, even though such a derivation is no more demanding mathematically or conceptually than the other issues discussed in the book.
   
   In sum, this book should appeal to any mathematically literate non-physicist who wants more than just a superficial introduction of Einstein's special relativity.

2 comments about Superstring Theory: Volume 2, Loop Amplitudes, Anomalies and Phenomenology (Cambridge Monographs on Mathematical Physics).

1. Volume I of "Superstring theory" presented the fundamentals of string theory. This book builds on those fundamentals and explores the possible observable consequences of string theory. The subtitle "Loop amplitudes, anomalies and phenomenology" provides a good high level view of the content.
   
   While the first volume demonstrated that string theory gives general relativity in the low energy limit, this volume explores some of the possible string theory implications in particle physics and how six of ten dimensions get compactified leaving the familiar four spacetime dimensions.
   
   The first two chapters cover one-loop diagrams in bosonic and superstring theories. The tone is similar to the tree level scattering amplitudes calculations done in volume I. The amplitudes are calculated for both open and closed strings (which of course must be included when you have open strings that interact), the important concepts of moduli space and orbifolds are introduced here. Among the interesting results for the bosonic string are an additional argument for D = 26 and the appearance of an ultraviolet cutoff for the cosmological constant.
   
   Following this is a lucid discussion of anomaly cancellation in Type I theory and path integral methods. Anomaly cancellation in Type IIB theories is considered later in the book, the subject of anomalies reappears throughout the remainder of the book.
   
   The phenomenology discussion starts by studying the low energy effective action. The supersymmetric gauge fields are examined for various string symmetry groups. The background in differential geometry needed to understand gauge theory, as expressed in the language of forms, is presented in an earlier chapter. The gauge fields that arise from compactification are treated in the next chapter, along with anomaly cancellation in four dimensions.
   
   This is followed by a very good, albeit brief, chapter on algebraic geometry. This is obviously not a comprehensive introduction, it sticks to the aspects that are relevant for string theory, for example Calabi-Yau spaces and Hodge numbers. The final chapter uses this mathematical machinery to explore the consequences of geometry of the compactified space may have for particle physics in our four spacetime dimensions.
   
   In my opinion this book holds up even better than volume I, no small feat, especially the latter parts of it. I think anyone specializing in string theory should still consider this required reading. If their emphasis is on string theory as a grand unified theory, or other implications of the low energy limits of string theory, then there's likely little doubt this is required reading.



2. This is a quintessential text for anyone who wishes to master the area of String Theory. I would say however it is not an introductory text but something one refers to after one has a rudimentary background in Quantum Field Theory as well as string theory; it is well written and contains a very thorough treatment of the modern knowledge we have about String Theory.