Book Description
This should prove to be the definitive work explaining van der Waals forces, how to calculate them and take account of their impact under any circumstances and conditions. These weak intermolecular forces are of truly pervasive impact, and biologists, chemists, physicists, and engineers will profit greatly from the thorough grounding in these fundamental forces. Parsegian has organized his book at three successive levels of mathematical sophistication, to satisfy the needs and interests of readers at all levels of preparation. The Prelude and Level 1 are intended to give everyone an overview in words and pictures of the modern theory of van der Waals forces. Level 2 gives the formulae and a wide range of algorithms to let readers compute the van der Waals forces under virtually any physical or physiological conditions. Level 3 offers a rigorous basic formulation of the theory. ... Read more

Customer Reviews (2)

Teaching and Research and Van der Waals forces
I teach courses covering the fundamentals of surface and colloid engineering. The Parsegian textbook is ideal for either teaching a segment of 6 to 9 lectures or teaching an entire course on Van der Waals forces - I have done both. Moreover, there is also advanced material included that is important for applications that range from biomembrane physics to wetting phenomena. Even the price is right!
This is an excellent book in every way.

Every science library should have two copies of this book.
This book is the best ever written about Van der Waals forces.Parsegian is the world's expert on this subject, which is essential for an understanding of physical biology and much of chemistry, engineering, and physics. Parsegian writes superbly and clearly.His book is fun to read. Every biologist and every biophysicist should get a copy. Every science library should have at least two copies of this book. ... Read more

Book Description
This book is a complete guide to the current state of geometric algebra with early chapters providing a self-contained introduction. Topics range from new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors, the structure of the Lie groups, non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. ... Read more

Customer Reviews (5)

makes your head buzz...
I'm reading this book somewhat in parallel with Hestenes' New Foundations for Classical Mechanics. Both are fantastic books (Hestenes' predates this one), and in some parts they are complementary, while of course they overlap in the foundations and many special topics. What is so fascinating about Geometric Algebra and Calculus? I think it's mainly the recognition that many seemingly complicated theorems of mathematical physics really become much clearer - in a sense of getting a guts feeling about the geometry. The method opens a way to look at the same thing from totally different angles: If one can't imagine something based on geometric arguments, one can take the presented formalism and translate it back into geometry, and suddenly things become clear.
Is the book (or that by Hestenes) basic and easy to understand or are they difficult? Certainly they require some work by the reader. To follow the entire book, one really can't do without learning to master the formalism of geometric algebra, which is simple, yet sometimes bizarre. I suspect though that it is only bizarre to the one who "knows it all" already: The student or scientist who has grown familiar with vector spaces, matrix notation and wiggling around with tensor notation, needs to go through the same exercises as the bloody beginner to whom even the idea of a vector may not be clear. In fact, the beginner could be at a real advantage to not being poisoned by vector calculus. For example, take the very basic notation for a geometric product of two multi-vectors: ab = a.b + a^b (the sum of inner and outer product). What's so confusing about it? Nothing, really, after one really understands what "+" here means. But it happens often enough that one only thinks about this product in terms of the right hand side of the equation, because those are totally familiar for anyone who took basic linear algebra, and then ends up making simple things complicated again. I must say that it was like loosing shadows from the eyes to see how the formulations in this book and Hestenes' work explain so well why it is that the quantum mechanical psi function needs to be complex, or better yet what really the i means in physics, and how the entire set of Maxwell equations (all 4 of them) are one simple continuity equation. That's the kind of thing that makes your head buzz. I'm not done with these books, but I have a clear feeling that in the end I will have an entry point to understand QM and parts of general relativity not just formally (especially QM) but really develop a guts feeling for it.
One thing that I'm still a bit missing in any of the books related to geometric algebra is classical continuum mechanics. This may be so because many of the authors are immersed in fields related to cosmology. In this book, one can find a tiny little bit also about elasticity (linear and nonlinear). However, I keep wondering what it would be like to reformulate the entire underlying theory of continuum mechanics (about deforming solids, elastic or viscoelastic or plastic, about fluid flow, about polarized materials, biological active materials, etc). Could something new be learned? I bet it could!

Provides a very interesting point of view
Provides a very interesting point of view, absolutely necessary for grasping the bolts and plumbing of modern physics.

The material covered was not present in other texts that I had a look at so this book serves as a good corner stone to build advanced undergraduate and graduate courses on.

A powerful mathematical language for physics and engineering
This is a well-written book on a very interesting and important subject: geometric algebra (GA) is a powerful and elegant mathematical language -- based on the works of Hamilton, Grassmann and Clifford -- that is especially well-suited for spacetime physics and several fields of engineering.

The authors adopt David Hestenes' viewpoint of a graded GA as a unified mathematical language that is coordinate-free, thereby stressing the fundamental role of geometric invariants in physics.

In fact, the elementary vector analysis -- which pervades almost all undergraduate (and even) graduate approaches to electrodynamics -- finds its roots in the misguided Gibbsian approach: Gibbs advocated abandoning Hamilton's quaternions and just work with scalar and cross products of vectors. However, the cross product has a major flaw: it only exists in three (or seven) dimensions -- if we require that (i) it should have just two factors, (ii) to be orthogonal to the factors, and (iii) to have length equal to the corresponding parallelogram.

Electrodynamics and relativistic physics, particularly, are elegantly presented through GA and otherwise cumbersome calculations may be circumvented in a simple and insightful way.

Mainstream physics and engineering cannot overlook GA anymore.

Compared to what ?
This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.

Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).

Geometric algebra IS a practical and natural (canonical) tool for formulating physical and mathematical problems in homogeneous spaces in a fully covariant fashion. But more importantly, you do not need to understand all those words in order to benefit from it, and this book is an excellent place for physicists of all stripes to start.

Articulate Path to the Future
The quality and importance of this book could hardly be overstated.Geometric algebra might casually be considered the "correct" generalization of linear algebra.By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles.Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors.The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying.Geometric algebra is all that and much more.By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises.It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry.Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.

Geometric algebra is a great theory, one of highest importance.It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow).This book is an especially good place to begin study.It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation.The economy and elegance of the geometric algebra itself allows this one substantial but not enormous book to reveal great insights into many branches of study, from differential geometry and its applications to gravity theory to quantum mechanics and classical mechanics.

If I had no books in my library, I would purchase a Bible.If I had only the Bible in my library, I would purchase this book next.I would certainly study this book in all detail before making a third purchase.My library already has several books in it.None of them will be read further until I finish every line, every exercise of this book.It's an important theory, and it is explained in a very useful and articulate way.This would, of course, be entirely expected if the authors were from Oxford University.Since they are only from Cambridge, we might not have expected as much, but we got it, nonetheless. ... Read more

Customer Reviews (1)

A nice classic.
This little book has become a kind of classic through the years, not only because of the reputation of the author, well known physicist Francis Bitter (1902-1967), but also for the carefull presentation of the facts and the stimulating examples given to clarify the exposition. The book is not a textbook on electromagnetism, neither an introductory text to the topic. It is a survey of Bitter's work on magnets from the early 20's on, and its principal object is to show how science (here exemplified in magnetism) is constructed by day-by-day work and efforts. The book is divided into seven chapters, which present a mixture of scientific description and personal anecdotes. The first chapter presents two problems that reinforced Bitter's determination to become a scientist. These problems, which are obviously discussed only at a very superficial level, are a heat flow problem and the bending of light rays by the sun's gravitational field (the reader will immediately associate this problem with the experimental verification in 1919 of Einstein's predictions). The second chapter introduces the basic concepts on magnets, mixed with the description of Bitter's experience at Columbia and that finally led him to this discipline. The close relation between electric fields and magnetism is explained by some illustrations (e.g., commenting on the difficulties of describing the magnetic attraction in dependence of the distance), as well as the empirical evidence on the nonexistence of magnetic monopoles (even if later chapter comment on nuclear magnetism, those interested on Dirac monopoles will search in vain for this notion in here, for there is no allusion to this fact in this book). After these introductory facts, the author focuses on the subject of his Ph.D. dissertation, the magnetic susceptibility of gases. Specifically the description of the experimental procedure to determine the susceptibility is of interest, presenting two types of apparatus that could be used, but from which only the second is actually of use to obtain accurate measures. Even today, the detailed discussion of these two possibilities would be a good question during a lecture. Some comments on paramagnetism and the relation to quantum theory are made. In chapter four the author describes how he came to be interested on ferromagnetism, and how his employment at the Westinghouse Company allowed him to become of the leading experts in this discipline, at those days in his beginning. The Curie temperature and demagnetization are explained, as well as how these questions lead to think of magnetic domains, and their experimental visualization by quite simple methods. The followingchapter resumes Bitter's work between his join of the MIT and the beginning of WWII, in constructing and designing of strong magnets. Kapitza's magnets are revisited, which gives the author the opportunity to develop his own ideas concerning the improvment of magnets, mainly in the direction of permanent magnets. This part is specially nice, since it enumerates the problems, doubts, material obstructions and frustations of scientific work, requiring constant actualizations and studies of theories thought independent of the problem being analyzed. An important fact is that Bitter does not hesitate in recognizing his errors (usually a rare thing in autobiographies), and how he had to adapt to the circumstances. Chapter six is a short résumé of the experience during the war, focusing mainly on the problem of degaussing ships to fight magnetic mines. It is worthy to be read, in order to see what ingenious methods were develop to protect ships from being destroyed by mines. The last chapter describes the problems Bitter chose to study after the war, and in which he was still immersed when writing this book (1959): nuclear magnetism. Although the material presented can only be a superficial vision, it is of interest in view of the important advances in this discipline since the beginning sixties. The magnetic distribution of nuclei is illustrated, and some important achievements of Bitter's reserach group exposed (at that time not explained yet by the theorists). Here the author shows how nuclear magnetism forced him (and others) to consider also other theories in order to obtain fruitful results. The final part of this chapter is devoted to some personal disquisitions, which, inspite of the fourtyyears ellapsed, have not lost in actuality.
Resuming, a nice book which shows the personal side of scientific activity, and exposes the real path for ideas and improvements that usually get lost when translated to textbooks. A very remarkable text, whose only fault is that his has not been reprinted. ... Read more

Book Description
Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses. ... Read more

Customer Reviews (3)

The best book on the subject
Before discovering the new book my Marian Fecko I thought I know all that I need about differential geometry (I co-authored a monograph on this subject myself). I had my favorite books: Kobayashi-Nomizu, Bishop-Crittenden, Sternberg, Michor, Abraham and some more. Yet "Differential Geometry and Lie Groups for Physicists" was a completely new experience. It is written with a "soul" and covers topics that are important but missing in other books. As I was working on a paper dealing with torsion, I emailed the Author with some of my ideas and questions and got an instant answer.

Readers looking for explanations and geometrical interpretations of the abstract concepts will certainly find this book irreplaceable. Lie and covariant derivatives, parallel transport, Hodge operator, Cartan's moving frame method, Laplace-Beltrami operator, Lie groups, Maxwell equations, Clifford algebras and spin bundles, SL(2,C), Dirac operator, Momentum map etc. etc.- all introduced and explained in a concise yet clear way, with exmaples and exercises.

This book should find its place on the bookshelf of everyone interested in geometrical concepts required for understanding contemporary theoretical physics.

I recommend this book to all students and professionals. It should find its place in every university library.

Just one warning: certain mathematical symbols did not find their way to the "Index of frequently used symbols" at the end of the book. The reader trying to read the book starting from p. 600 may find it necessary to spent some time going through the earlier chapters to find out the meaning of a given symbol.

Differential geometry
Marian Fecko's textbook covers well fundamental elements of modern differential geometryand introduction to the Lie groups (not only) from geometrical point of view. Geometrical formulations of the classical mechanics, gauge theory and classical electrodynamics are discussed.

The textbook expects the reader to be familiar with mathematical analysis on the level of the standard course usual in the physics undergraduate study programs. Understanding of the parts dealing with physical applications (classical mechanics and electrodynamics) expects knowledge of fundamental principles of these subjects. Organization of the book allows the reader to concern on particular part, i. e. understanding of later parts doesn't require reading of all previous parts (reading of parts concerning on the classical dynamics does not require reading of parts dealing with electrodynamics). However, relations between different subjects of the theory are explained instructively.

The main advantage of this textbook is that reader "builds" the subject himself by solving the exercises usually appended by hints. It makes all the elements of the theory natural to the reader during study. This way is a little bit more time consuming when compared with other textbooks dealing with this subject. It provides good starting point for study of mathematical aspects of the general relativity and field theories. I recommend this book to everybody who wants to understand fundamental concepts in differential geometry in detail.

not for starter or self-learning
The book covers a good range of topics in Differnetial geometry with lots of exercises. One literarily has to do the exercises to develop the concept. Ecah chapter ends with a concise summary of the key equations. The problem is that all the exercises are mixed with the main context. It lacks any exposition or concept development for most of the topics, no definition, no prove, and every page is filled with exercises.This style make it difficult for someone to learn the subjects the first time or to use it as a reference.

Separately, there are too few graphs to assist the reader to visualize the ideas. The prints are also small making it hard to read.

Nakahara's book (Geometry, topology and physics) is a much better choice on the same subject.



... Read more

Book Description
This unique collection of problems and solutions, selected from examination and tutorial questions used in the University of Bristol, is the first book of its kind to address the 'art' of problem solving in a truly constructive manner. The reader is encouraged to apply basic physical principles, judicious assumptions and approximations, and simplified 'models' of complex situations, and to consider the limitations of the resulting solutions - in short to 'think like a physicist'. The problems are taken from all branches of the subject, but most deal with topics that are essentially elementary, and should therefore be accessible to first and final-year undergraduates alike. The inclusion of a full set of solutions ensures that the student cannot become 'lost' in a problems, and can therefore avoid much of the frustration associated with problem solving 'in the dark'. Students who use this book will no longer be faced with the feeling of helplessness - even despair - experienced upon opening an examination paper and being confronted with a seemingly impenetrable set of questions, apparently designed to foil even the the most diligent and attentive of pupils. They will no longer complain 'They didn't tell us that in lectures; how were we supposed to know that?' and will be confident when faced with problems outside their direct experience. As a teaching and learning aid, this book will prove to be an invaluable acquisition for lecturers and students in physics and the physical sciences, and should therefore not be missed. ... Read more

Book Description
This is the first book to present both classical and quantum-chemical approaches to computational methods, incorporating the many new developments in this field from the last few years. Written especially for "non"-theoretical readers in a readily comprehensible and implemental style, it includes numerous practical examples of varying degrees of difficulty. Similarly, the use of mathematical equations is reduced to a minimum, focusing only on those important for experimentalists. Backed by many extensive tables containing detailed data for direct use in the calculations, this is the ideal companion for all those wishing to improve their work in solid state research. ... Read more

Book Description
This new adaptation of Arfken and Weber's bestselling Mathematical Methods for Physicists, Fifth Edition, is the most comprehensive, modern, and accessible text for using mathematics to solve physics problems. Additional explanations and examples make it student-friendly and more adaptable to a course syllabus.

KEY FEATURES:
· This is a more accessible version of Arfken and Weber's blockbuster reference, Mathematical Methods for Physicists, 5th Edition
· Many more detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems
· More frequent and thorough explanations help readers understand, recall, and apply the theory
· New introductions and review material provide context and extra support for key ideas
· Many more routine problems reinforce basic concepts and computations ... Read more

Customer Reviews (5)

Perfect
This book is perfect for my needs.It is just what I needed to review my mathematical skills for my Master in Physics.

Weak on rigor & physical insight = bad book
Strengths:
- Fairly complete coverage of the various properties of special functions.The introduction of these subjects is not good, but one could use it as a refrence for formulas.

Weaknesses:
- Topic selection and rigor are weak.Many important areas of mathematical physics are skipped over, or short changed.For example, the section on tensors is far too short.In addition, everything is introduced in index notation instead of coordinate free form.Also, the group theory section is very weak (not to mention short).The rotation group and lorentz group are discussed briefly, but there is no systematic introduction to lie groups or other important topics.
- The book seems to focus on special functions, and solving differential equations.However, it does not introduce hilbert spaces well, and therefore the presentation seems like a bewildering array of bessel this and fourier that, without anything to tie it all together.

Overall, I'd say the book sacrifices depth by covering too many topics.If you want to really succeed you're going to need a full course each on linear (& some multilnear) algebra, mutlivariable calc & vector analysis, differential equations, complex analysis, differential geometry and group theory.If you want a condensed version, get byron and fuller.It's written systematically, and strikes (in my opinion) a perfect balance between rigor and pragmatism.

Great undergrad physics major book!
This undergraduate text makes Arfken really accessible. The new examples are great and most are from various fields of physics. This has helped me in my mechanics, E and M, and quantum mechanics classes. The long index is complete and really helps to find things quickly. The chapter on probability & statistics explains concepts especially well.

Better Overview then Book
This book is much better as a reference book for someone who already understands the material then for a student just learning.The book covers everything from Coordinate Systems to Calculus of Variantions, PDQ's, and Special Unitary Groups in highly dense sections, with little or no examples.

The problems are extraordinarly tough, and they seem disjointed, lacking any real focus and coherence, exp. towards the front of the book.Once you get past the physics in the first part, and into the math section of the book, it slows down, and really explains ideas, as well as providing excellent problems to work.

I would recommend this book as a reference, but there are better books out there.For reference, I would also recommend Schaums Outlines; and for a text book, I would recommend David Hilbert's Mathematical Methods Vol I, and Vol II.

Better as a reference
I used this book for an undergraduate math methods for physicists course.While in the class I found it very difficult to learn anything from it, as it is rather dense.I found that most websites I looked to for help cited the book though.Now I find this book to be a very useful reference.It's definitions are fairly concise and topics are not spread throughout the book.Bottom line: great reference, poor learning tool. ... Read more

Book Description
The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. This up-to-date volume provides the essential mathematical and computational education for students, researchers, and practicing engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. He concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers. ... Read more

Customer Reviews (1)

Highly recommended
Of all the "mathematical methods" or "applied mathematics" books
on my shelf, this is the one I find myself turning to most often.

There are many other books where you can look up, say, the
orthogonality properties of some "special function," but for an
authoritative explanation of fundamental mathematics as used
in physics today -- especially computational physics -- Cantrell
is excellent.

I often have to check with Cantrell to get an answer to questions
like "Is this result in this other text true in general, or only
in the special case that its author describes?".I never have
to double check to see to what extent the results in Cantrell
apply -- he makes things like that quite clear.

Cantrell has included a healthy dose of linear algebra and
functional analysis in his text, at the expense of some of the
chapters in more traditional mathematical physics texts, such as
those on contour integration or special functions.

However, examples of the use of special functions are sprinkled
liberally thoughout the text.And although the chapter on that
subject is mostly about Bessel functions, Cantrell's discussion
of Bessel functions is, typically, different from and more
insightful than conventional treatments.

My quibbles with the book have to do not with its content, but
with "first edition" glitches -- a figure here or a typo there.
And some sort of bug in the index preparation process left many
of the page numbers referred to in the index "off" by a page
or two.On the other hand, the hardcover edition that I have
lays open nicely on my desk, and after heavy use the binding
has not broken, and no pages have fallen out.

It would be nice if there were an appendix of "Answers to Exercises,"
or maybe a "Student's Guide."However, many of the exercises
are of the "Show that ..." variety, so the lack of such an appendix
is not nearly the drawback that it might be.

Overall: Excellent book, highly recommended. ... Read more

Book Description
This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers. ... Read more

Customer Reviews (1)

Mixed feelings
Lie groups and Lie algebras permeate most parts of theoretical physics. Every student in physics should have some basic notions of the subject as it sometimes tends to have unsuspected applications.

The first three chapters of this book include exemples and motivation for the more formal aspect of the Lie theory. Those are also meant to set the notation used later throughout the book. Topics covered should be well-known from a senior undergraduate student with a good background in quantum mechanics (harmonic oscillator, the rotation group) and particle physics (mostly the "zoological" part of it : classification of particles, the eightfold way and so on).
From chapter 4 on, the Maths definitely take the most prominent part of the stage. Chapter 4 is a reminder of basic notions in algebra, as covered in an undergraduate course in algebra and classical groups.
Chapter 5, on representation, should not be a challenge to the physicist.
The core of the subject is presented in chapter 6, where the idea of the Cartan-Weyl basis is given a nice presentation. This chapter is a little bit more demanding. Some statements are not proved. However, a committed student in physics, should be able to devise proofs for him/herself.
Chapter 7 is particularly enjoyable, dealing with Dynkin diagrams and the classification of finite simple Lie algebras, and introducing infinite dimensional ones. The way Kac-Moody algebras appear, through relaxing the axioms of the Chevalley-Serre construction should be appreciated. Also, physical exemples are to the point.
However, beginning with chapter 12, the wrongs of this book become somewhat annoying. For instance, in chapter 12, the authors of this book freely speak of Verma modules, highest weight representations, while these concepts are to be introduced and properly developped in later chapters. I found this chaffing from an introductory book. From chapter 12, it seems that the reader is to gently follow and accept the statements made by the author, without encountering much proof or hint to this all.
Things come more acceptable in later chapters only, where invariant tensors and other things more familiar from a physicist with no previous acquaintance to Lie algebras, are exposed.

All in all, a good book for some parts of it but whose value could have surely been enhanced by adopting a more pedagogical presentations. Some proofs to key facts in the more "exotic subjects", would have been welcome, too. All the more, that some chapters of this book did not require much work from the authors, as it seems that they were taken from Dr. Fuchs "Affine Lie algebras".
Hopefully, welcome additions will be added to a further edition.
Beginners or readers with a casual interest in Lie algebras should better learn it from another source.
... Read more

Book Description

Customer Reviews (1)

A very helpful book
This book presents to the lector in acomprehensive way the necesary mathematical methods needed by any physicist, engineer or student. It includes themes such as elementary vector calculus, matrix algebra andtransformations, a very extensive study of boundary value problems,elementary applicationsof the Laplace Tansform, Integral Transforms,Variation and Perturbation Methods, Elements of Probability Theory, amongothers.Each point is well exposed, with many explamples and problems(although it doesn't provide the answers). A defect may be the fact thatsome points (although few) are not fully developed, and in some cases onewill probably have to read a more basic-level book on those points (As afreshman, it happened to me that to understand chapters 7 and 8, aboutfunctions of a comples variable and calculus of residues, I had to read anintroductory book on complex variable). It's develop of many math topicsand it's application to Physics and Engineering and the independance ofmany chapters from the others, makes this book a very helpful one. ... Read more

Book Description
How did Andrei Sakharov, a theoretical physicist and the acknowledged father of the Soviet hydrogen bomb, become a human rights activist and the first Russian to win the Nobel Peace Prize?In his later years, Sakharov noted in his diary that he was "simply a man with an unusual fate." To understand this deceptively straightforward statement by an extraordinary man, The World of Andrei Sakharov, the first authoritative study of Andrei Sakharov as a scientist as well as a public figure, relies on previously inaccessible documents, recently declassified archives, and personal accounts by Sakharov's friends and colleagues to examine the real context of Sakharov's life.In the course of doing so, Gennady Gorelik answers a fascinating question, whether the Soviet hydrogen bomb was really fathered by Sakharov, or whether it was based on stolen American secrets.Gorelik concludes that while espionage did initiate the Soviet effort, the Russian hydrogen bomb was invented independently. Gorelik also elucidates the reasons that brought about the seemingly sudden transformation of the top-secret physicist into a public figure in 1968, when Sakharov's famous essay "Progress, Peaceful Coexistence, and Intellectual Freedom" was distributed in samizdat in the USSR and smuggled out to the West. Recently declassified documents show that Sakharov's metamorphosis was caused by professional concerns, particularly regarding the development of an anti-ballistic missile defense. An insider's view of how the upper echelons of the Soviet regime functioned had led Sakharov to the conclusion that the goals of peace, progress, and human rights were inextricably linked.His free thinking and free feeling were manifested in his hope that scientific thought and religious perception would find a profound synthesis in the future. ... Read more

Book Description
This edition of the invaluable text Modern Differential Geometry for Physicists contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made.

These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics.This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory.

The volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry. ... Read more

Customer Reviews (2)

Good, with problems
Wow! What a great Table of Contents.It has all the stuff I've been wanting to learn about.So I bought the book in spite of seeing only one review of it.After one day, I'm now only at page 26, but I already have read enough to make some comments about it.
The main point about this book is that it is, as the author specifically states, LECTURE NOTES, not, I repeat, not a textbook. What are the implications of this (outside of a somewhat more chatty style than a textbook)?["chatty" isn't quite what I mean; "smooth" might be a better word'] There are two which are noticable to me.1) A lot of math knowledge is taken for granted.2) It has a somewhat sloppy style to it.

Regarding point one, make sure you have a lot of math under your belt before picking up this book.By page 18 the author uses these terms without defining them: Differentiable Manifold,semigroup, Riemannian Metric, Topological Space, Hilbert Space, the "" notation, vector space, and Boolean Algebra.Fortunately for me, I have a fairly extensive math education, and self-studied Functional Analysis, so I wasn't thrown for a loop;but for many others -- brace yourselves!

Regarding point two, Here are two examples:
1) Here is a quote: "The collection of all open sets in any metric space is called the topology associated with the space."Sounds like a definition to me!Fortunately the author gives a (sloppy) definition a few lines later.By the way, the only thing the reader learns about what an 'open set' is, is that it contains none of its boundary points.All the topology books I have read define open sets to be those in the topology.This is another point of confusion for the reader.In fact, points of confusion abound in that portion of the book.
2) On page, 17, trying somewhat haphazardly to explain the concept of a neighborhood, the author defines N as "N := {N(x) | x is an element of X}"This is already a little disconcerting: x is already understood to be an element of X.So he is saying that N is defined as N(x) (which he defines to be a collection of subsets of X).This is all he has to say on the matter until, on page 26, he writes "each N, an element of N(x)".Now N isn't bothN(x) and an element of N(x).This is a point which the author does not clear up.He then starts using N all over the place, yet the reader isn't sure of what he's refering to.

A couple of other things:
-When he defines terms, they is not highlighted, and are embedded in a sentence, making it difficult to find them later.
- The index is pitifully small. Typical for English texts, I know; but this *is* the 3rd millinium!

On the other hand, I have good things to say about the book, too.
I like his style of writing. If it were just more precise, it would be fine for me.I like it better than the normal higher math texts, which tend to be too laconic for me. Notice that I make a distinction between the somewhat chatty style, which I like, and the sloppiness, which is confusing. One can be chatty, yet clear. So far, the undefined math terms which I listed above were not central to the text; and one would not miss much by just reading past them. The author includes many 'comments' sections throughout the book.These are wonderful so far. They are full of comments and examples which really clear up a lot of points.His examples are very good, too, although he is very terse in stating them.The paperback is nice looking.The paper, font, etc. make for easy reading (except for the sub/super-script font, which is too small for me).

To wrap this review up, I had already pretty much learned the stuff covered in the book so far, but judging from what I have read, I will be able to learn a lot from the rest of it; and, unlike some other math books I have studied, the experience won't be too painful.
p.s. See other reviews of it on the UK Amazon site.

Very readable presentation of diff. geometry
I have found Isham's treatment of differential geometry very clear, while maintaining quite an abstract nature. Ishamtakes care to motivate hisdefinitions and include comments where comments are due. No problems areincluded but the book sometimes omits the simpler results and lets you workthem out by yourself. A very readable introduction indeed. ... Read more

Book Description
Philip Morse has surely been one of the most versatile of American scientists of his generation, the first to be trained largely in his own country. A scientific generalist, he has made significant contributions to atomic physics, quantum mechanics, plasma physics, astrophysics, acoustics, machine computation, and operations research. His life-long commitment to teaching, through his authorship of a series if standard-setting textbooks and through his personal guidance of unnumbered individual students, has extended this scope to include thermodynamics, statistical mechanics, and the methods of theoretical physics as well.

Moreover, as this autobiography relates at a fast-moving pace, Morse has also been involved in the high-pressure concerns of war research, scientific administration and consultation, policy formation, the education of key groups and wider publics beyond the classroom, and the real-world utilization of scientific techniques and discoveries.

For all these accomplishments, Morse writes that his experience as a scientist and as a participant in the affairs of his time "has been at the second, rather than at the top, level." It may be that this circumstance of being neat, rather than at, the top makes this autobiography more, rather than less, relevant to other and younger scientists, to those considering a life in science, and to general readers curious as to what such a life is really like. Only a miniscule few reach, say. Einsteinian levels, and their lives and work tend to be unique unto themselves; what Morse reports is truer to the experience of the great majority of the members of the scientific community. While his actual accomplishments, his range, and his eminence certainly far exceed those of a "typical" scientist, they do so more in degree than in kind.

Morse's style is straightforward and nontechnical, direct, and personal. Some of the lighter moments and revealingly human incidents of his experience are recorded along with the problems and breakthroughs in the near-private world of pure science and the public worlds of policy, high-level consultation, and practical applications. ... Read more

Customer Reviews (1)

fascinating story of a professional life
Morse is a fairly well-known mathematical physicist (that is, he was famous enough to be known outside his field), and this is his autobiography. I'm reviewing it from memory, since I read it when it first came out in the 70's, but it made an impression on me. He's literate, and comes across as very straightforward (although perhaps he just maintains this pose for the duration of the book -- I never met him), and he was involved in many fascinating areas.

In addition to his work in physics (among other things, he was the primary or sole author of a some standard graduate level textbooks), he was one of the "inventors" of operations research while working for the Navy during WWII. The story of the atomic bomb research is pretty well documented, and the story of the development of radar can be read in more than one place, but this is the only account I've seen of "the rest" of the vast amount of R&D work that was funded by the War Department during WWII.

Among the interesting anecdotes he relates, he was one of Feynmann's teachers in college, and Feynmann's father came to ask him (Morse) if his son (Richard) should go to grad school in physics. Morse was perceptive enough to assure the father that his son had what it took...

If you are interested in personalized accounts of the history 20th century science, this book is for you. It's similar in scope to Ulam's book about the atom bomb, but much better written, and the author comes across as quite human (which often doesn't happen in autobiographies of scientists). ... Read more

Book Description
This book is ideal for anyone who would like to read about the lives of some of the most remarkable physicists born since the second half of the seventeenth century. Each of the fifty-five physicists profiled have made important contributions to physics, through their ideas and teaching, or in other ways. The biographies are arranged chronologically by the physicists' dates of birth, so that, when read in sequence, they convey how physics developed over time. However, the book emphasizes their varied life stories, not the details of their achievements. Ioan James is Professor at the Mathematical Institute, University of Oxford. He is the author of Remarkable Mathematicians (Cambridge University Press, 2003) and Topological and Uniform Spaces (Springer-Verlag, 1999). ... Read more

Customer Reviews (1)

Only on physicists' lifeand almost none on their achievement!!!
Of course I understand that Ioan James's intention of writing this book is to give us a more " human " aspect about the physicists and not a work on the theory of physics. I fully agree. However he should at least state
at least very briefly about the achievement of the great physicist!! Take for an example, in describing Ampere, he does not even mention about the Ampere's law!!! I think at least in describing various physicists, he should at least state briefly about what contribution of those hysicists. Just on sentence about the equation of the laws would make this book far more interesting! Otherwise, just mention the date of birth, when the phyicist went to univerisity, when he married, when he died etc.I would ask, then what make this physicists worthy of a brief biography and separae them from just an ordinary people????????????????? ... Read more

Book Description

Customer Reviews (1)

An excellent overview of discoveries in physics.
I have read a fair amount of books on physics and found this one to be very enjoyable. Gamow keeps things pretty simple (until the end when he starts talking about his specialty) and very accessible. He is careful that the math is sequential; he always builds on previous examples to take you to the next step.

The book was published in the 60's, so there are many recent discoveries missing, but you need to know your history of physics to see how we got where we are.In fact, I found that this bookshowed just how new all of our current theories are and that there is promise for many new things on the horizon. ... Read more