Book Description
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
Customer Reviews:
Excellent math reference for physicists.......2007-08-06
As the title says, it's one of the best books for mathematics in physics. Not simple at first glance (not indicated for first students, I guess), but good to review some math...
Great Physical Mathematics.......2007-07-31
Great mathematical physics book. I bought it as a supplement text for a mathematical physics course as well as help in quantum physics course. Got me through a lot of Quantum homeworks. I still use this book as a reference for math and physics concepts. The ordering of the book is a little weird and skips the some of the basic concepts in linear algebra but explores a wide variety of other topics including Green Functions, Cauchy-Riemann, Fourier analysis and transforms, Dirac notation, ect. At the end of topic the book works through examples. A must have for physicist, engineers, and mathematicians.
astonishing!.......2007-06-08
this book chose the best way to convey the mathematics behind a physical idea just by proving it through the mathematics involved . With that , one has a lucid idea about the language of physical laws . I can simply assure anybody who wants to buy this book that it is worthy .
The real deal........2007-05-16
Over my head, but clearly a solid rung in the ladder for those who are capable of mastering quantum physics. Not that I couldn't - it would just take 10-20 years that I don't have.
Dated but a Great Reference.......2007-03-20
There's hardly anything in this book (two volumes bound as one) that you won't find of use sometime in your career as a physicist or engineer. I especially liked the authors' lucid treatment of Green's functions, a subject that for some reason keeps escaping my aging mind. Basically an undergraduate text but can also be used as a beginning graduate reference.
Average customer rating:
- A unique, masterful and enjoyable book for graduate student in physics
- I would recommend foundations of mechanics by Marsden
- Best book on CM
- Encyclopedic
- The best, but challenging for not-mathematicians
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Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics)
V. I. Arnold
Manufacturer: Springer
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Ordinary Differential Equations
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The Geometry of Physics: An Introduction, Second Edition
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Course of Theoretical Physics : Mechanics (Course of Theoretical Physics)
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The Classical Theory of Fields, Fourth Edition: Volume 2 (Course of Theoretical Physics Series)
ASIN: 0387968903 |
Book Description
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Customer Reviews:
A unique, masterful and enjoyable book for graduate student in physics.......2007-02-08
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.
I would recommend foundations of mechanics by Marsden.......2006-01-07
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.
Best book on CM.......2004-02-26
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.
Encyclopedic.......2002-05-08
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.
The best, but challenging for not-mathematicians.......2001-10-21
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.
Customer Reviews:
Great book!.......2005-04-26
I'm taking AP Physics C in high school and this has proven to be a valuable book. It takes time to do the problems and read his solutions. But it's worth the time. Helps you built intution.
Missing a Topic?.......2000-12-05
This book was great. Elby's explanations of physics are uncomparable with textbooks'. However, I was really surprised at the fact that a whole topic was omitted from both volumes of his book. He seemed to have omitted "THERMODYNAMICS," a hardcore topic of physics. I thought that was unbelievable, but hey what can I say? Only 1/3 of my upcoming physics final will be on THERMODYNAMICS. Blah!
He explains the principles clearly but.......2000-05-02
At times the font size for an equation appears to be about the half the font size of the other equations on the page. This happens sporadically in the book. Also, some of the labeling of the diagrams have an even SMALLER font size. This is annoying. Very annoying when you end up looking at the equation several times. The irony is that I took this physics course while I was in the navy via correspondence. The above was on the syllabus of thing not to do! In the end I can say this book helped me pass the course with a "B". He does show you how to approach a problem different ways. And the tests he has on the book ... excellent.
Excellant commentary but get a magnifying glass.......2000-04-18
The commentary is very good. The author shows different approaches to solve physics problems and which approach is better (and why). What is the downside? You will see an equation with a smaller font size. There is an inconsistency in how the smaller font size is applied. The commentary may be a page long with several equations. Usually one equation has the smaller font size. It appears to decrease to a #8 font. It does not stop there. Some of the labeling of the drawing is smaller. Looks like #6. This type of activity would not endear you to the TA or Prof. as they grade your exams. Hopefully, the next edition comes enclosed with a magnifying glass.
You should get this book........2000-03-01
This explained things much more clearly than my textbook. If you're taking physics you should get it.
Average customer rating:
- Terse and unhelpful - a dreadful book - avoid like the plague!
- Excellent Condition
- Maybe good for a reference, but not the best first source
- The standard, but maybe not the best
- 2 Books in one
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Statistical Mechanics
Donald A. McQuarrie
Manufacturer: University Science Books
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Introduction to Modern Statistical Mechanics
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ASIN: 1891389157 |
Book Description
Now available from University Science Books at a much lower price, this classic textbook has never been rivaled. It is ideal for a senior or first-year graduate level courses. Statistical Mechanics is the extended version of McQuarrie's 1984 text -- Statistical Thermodynamics -- now out of print. Although our printing of this book carries a 2000 copyright date, this is not a new edition. It is the original first edition, without any changes to the text (except preface). Despite its age, it is still a renowned and accessible introduction to the subject, containing a large number of chapter-ending problems for students.
Customer Reviews:
Terse and unhelpful - a dreadful book - avoid like the plague!.......2007-07-20
I was forced to use this singularly unhelpful book in graduate school. It was written in a terse, indigestible style; contained very few worked problems; left many important derivations or steps of derivations to the reader; had impossibly hard end-of-chapter problems - without solutions; and contained many typographical errors. Perhaps, as other reviewers have suggested, it would have been more helpful as a research reference, or as a textbook for students with a very strong background in undergraduate statistical thermodynamics. Do not attempt to use this book to learn statistical mechanics for the first time!
This review refers to the first edition.
Excellent Condition.......2007-01-19
The condition of the book I purchased was rated as very good on the Amazon web site, but its real condition was excellent. In fact, it is as close to being a new book as a used book can get.
Maybe good for a reference, but not the best first source.......2006-04-24
I am a engineering/physics student, and I used this book for a first year graduate course in statistical mechanics. The book contains a lot of information, and the chapters are extremely concise. In this, lies both the strengths and weaknesses of the book. I think that the short, too the point writing style makes this book an excellent reference. However, the relatively small amount of exposition made it hard to learn material for the first time from the book. Overall, I would not suggest this book as a first introduction to the subject. But i think that it could be a usefull reference for someone with some background in the subject.
The standard, but maybe not the best.......2003-07-03
McQuarrie's book is typically the standard text in many undergraduate and graduate programs, but I believe there are many other resources to learn statistical mechanics in a much clearer way.
I find the following things to be particularly annoying about the book:
1) The typesetting! The pages are very difficult to read, especially equations. It's a very old typeface and my eyes literally hurt after reading McQuarrie for too long.
2) Very few problems are worked out. Many important concepts that should involve more detailed discussion are simply left as exercises to the student. I believe that more peripheral results and extensions of fundamental material are better left as problems, as opposed to fundamental results.
3) The glaring absense of good discussion on spin systems (such as Ising magnets) and critical phenomena. These are VERY important topics in modern statistical mechanics.
I would recommend the following if you want to find good books on statistical mechanics:
1) If you want one comprehensive volume, use Linda Reichl's book.
2) If you are only interested in statistical thermodynamics, use David Chandler's book.
3) If you want both statistical thermodynamics and nonequatilibrium statistical mechanics, use Chandler and Robert Zwanzig's book.
Also, Kubo's statistical thermodynamics book is really good.
I really would not recommend McQuarrie. Save your eyes and get a more modern book with at least a better typesetting.
2 Books in one.......2003-03-23
This is a good book, but it's not a graduate text for the first half. If you're just reading it and not taking the class, buy Hill instead (it's $10). McQuarrie learned how to teach SM from Hill and it shows. The second half is a whole different story. It's research level material, but is perhaps out of date. Lastly, Karl Freed and Stuart Rice teach from this book, which should be worth far more than my review.
Book Description
Mathematica for Theoretical Physics:
Classical Mechanics and Nonlinear Dynamics
This second edition of Baumann's Mathematica
® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica
® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems.
The second edition has been completely revised and expanded into two volumes:
The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.
New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
The CD-ROM accompanying each of the two volumes contains Mathematica
®
notebooks as well as Mathematica
® programs. The notebooks contain the entire text of the corresponding volume and can interface with Mathematica
®. The examples given in the text can also be interactively used and changed for the reader’s purposes.
The Author, Gerd Baumann, is affiliated with the Mathematical Physics Division of the University of Ulm, Germany, where he is professor. He is the author of Symmetry Analysis of Differential Equations with Mathematica
®. Dr. Baumann has given numerous invited talks at universities and industry alike. He regularly hosts seminars and lectures on symbolic computing at the University of Ulm and at TECHNISCHE UNIVERSITÄT MÜNCHEN (TUM), Munich.
Book Description
Over 130 years ago, James Clerk Maxwell introduced his hypothetical "demon" as a challenge to the scope of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science, and links have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Since the publication of Maxwell's Demon: Entropy, Information, Computing in 1990, Maxwell's demon has been the subject of renewed and increased interest by numerous researchers in the fields mentioned above. Updated and expanded, Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing retains many of the seminal papers that appeared in the first edition, including the original thoughts of James Clerk Maxwell and William Thomson; a historical review by Martin Klein; and key articles by Leo Szilard, Leon Brillouin, Rolf Landauer, and Charles Bennett that led to new branches of research on the demon. This second edition contains newer articles by Landauer, Bennett, and others, related to Landauer's principle; connections with quantum mechanics; algorithmic information; and the thermodynamics and limits of computation. The book also includes two separate bibliographies: an alphabetical listing by author and a chronological bibliography that is annotated by the editors and contains selected quotes from the books and articles listed. The bibliography has more than doubled in size since publication of the first edition and now contains over 570 entries.
Customer Reviews:
The Second Law.......2007-01-16
A collection of articles that explain the Second Law of Thermodynamics by looking at its most famous violator. It contains articles by William Thompson (who had not yet been made Lord Kelvin), Leo Szilard, Charles Bennett, Rolf Landauer and a cartoon by Larry Gonick (a fragment of which, a grinning little demon sitting on Maxwell's shoulder, is on the cover). The modern solution to the paradox posed by the demon is that the erasure of previously stored information in order to make room for the result of the observation increases the entropy of the demon by at least as much as the entropy of the vessel is decreased. Read Feynman Lectures on Computation for more context.
Clear, complete, and well-organized.......2003-02-20
Maxwell's Demon 2 is one of the best books I've found in the field - the authors address key issues in a clear and engaging manner. This is an excellent and well-organized reference book and includes any number of original papers which are difficult to find through other sources. Highly recommended.
Average customer rating:
- SPAM and sph, a superior route to continuum solutions
|
Smooth Particle Applied Mechanics: The State of the Art (Advanced Series in Nonlinear Dynamics) (Advanced Series in Nonlinear Dynamics)
William G. Hoover
Manufacturer: World Scientific Publishing Company
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ASIN: 9812700021 |
Customer Reviews:
SPAM and sph, a superior route to continuum solutions.......2007-01-15
This excellent monograph, prepared by Professor Hoover with the help of his wife Carol, contains all that a reader needs to understand, develop, and use smooth-particle techniques for computer simulations of continua. Applications to solid deformation and to fluid flow display a variety of useful techniques for avoiding the usual pitfalls with standard sph.
Average customer rating:
|
Statistical Methods in Quantum Optics 2: Non-Classical Fields (Theoretical and Mathematical Physics)
Howard J. Carmichael
Manufacturer: Springer
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ASIN: 3540713190 |
Book Description
Statistical Methods in Quantum Optics 2 - Non-Classical Fields continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in the first volume
Statistical Methods in Quantum Optics 1 - Matter Equations and Fokker-Planck Equations: the difficulties these methods face in treating non-classical light are exposed, where the regime of large fluctuations – failure of the system size expansion – is shown to be particularly problematic. Cavity QED is adopted as a natural vehicle for extending quantum noise theory into this regime. In response to the issues raised, the theory of quantum trajectories is presented as a universal approach to the treatment of fluctuations in open quantum systems.
This book presents its material at a level suitable for beginning researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems. The text is complemented by exercises and interspersed notes that point the reader to side issues or a deeper exploration of the material presented.
Book Description
"Symmetry in Mechanics is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject...The first chapter presents a standard derivation of the equations for two-body planetary motion. Kepler's laws are then obtained and the rule of conservation laws is emphasized. ..... Singer uses this example from classical physics throughout the book as a vehicle for explaining the concepts of differential geometry and for illustrating their use. ... These ideas and techniques will allow the reader to understand advanced texts and research literature in which considerably more difficult problems are treated and solved by identical or related methods. The book contains 122 student exercises, many of which are solved in an appendix. The solutions, especially, are valuable for showing how a mathematician approaches and solves specific problems. Using this presentation, the book removes some of the language barriers that divide the worlds of mathematics and physics..."
---- Physics Today
Recent years have seen the appearance of several books bridging the gap between mathematics and physics; most are aimed at the graduate level and above. Symmetry in Mechanics: A Gentle, Modern Introduction is aimed at anyone who has observed that symmetry yields simplification and wants to know why. The monograph was written with two goals in mind: to chip away at the language barrier between physicists and mathematicians and to link the abstract constructions of symplectic mechanics to concrete, explicitly calculated examples. The context is the two-body problem, i.e., the derivation of Kepler's Laws of planetary motion from Newton's laws of gravitation. After a straightforward and elementary presentation of this derivation in the language of vector calculus, subsequent chapters slowly and carefully introduce symplectic manifolds, Hamiltonian flows, Lie group actions, Lie algebras, momentum maps and symplectic reduction, with many examples, illustrations and exercises. The work ends with the derivation it started with, but in the more sophisticated language of symplectic and differential geometry. For the student, mathematician or physicist, this gentle introduction to mechanics via symplectic reduction will be a rewarding experience. The freestanding chapter on differential geometry will be a useful supplement to any first course on manifolds. The book contains a number of exercises with solutions, and is an excellent resource for self-study or classroom use at the undergraduate level. Requires only competency in multivariable calculus, linear algebra and introductory physics.
Customer Reviews:
Most gentle introduction.......2006-03-22
Stephanie Singer's book is a service to all students who wish to learn modern aspects of mechanics for the first time.
A nice introduction to modern methods.......2005-02-20
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.
Poorly written.......2003-12-12
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.
A welcome book.......2002-01-26
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!
Average customer rating:
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Diffusion-Wave Fields: Mathematical Methods and Green Functions
Andreas Mandelis
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ASIN: 0387951490 |
Book Description
This book develops a unified mathematical framework for treating a wide variety of diffusion-related periodic phenomena in such areas as heat transfer, electrical conduction, and light scattering. Deriving and using Green functions in one and higher dimensions to provide a unified approach, the author develops the properties of diffusion-wave fields first for the well-studied case of thermal-wave fields and then applies the methods to nonthermal fields. The presentation, largely in the form of case studies directly applicable in a wide range of experimental methodologies, is intended for graduate students, professional scientists and engineers working in fields that involve diffusion waves, including thermal-wave, photothermal and photoacoustic spectroscopies, non-destructive evaluation, semiconductor and electronic device carrier plasma-wave characterization, and biomedical laser tissue diffuse photon density-wave diagnostics. The treatment requires no more mathematical background than a course in advanced calculus and mathematical analysis. Problems at the ends of each chapter complement the main text and some serve to extend the material to current research.
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