Mathematics of Classical and Quantum Physics
Mathematics of Classical and Quantum Physics
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 List Price: $24.95 Sale Price: $9.97 Availability: unspecified 
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Product 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.
Details
- ISBN13: 9780486671642
- Condition: New
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Rating
This book is a great summary of the essentials of applied math used in physics. (A lot of stuff I missed since I took mostly pure math classes.) It gives enough of a start to tackle something like Courant & Hilbert or Morse & Feshbach. Plus it sometimes has information useful enough to solve problems from Jackson.
At the price, nothing can beat it. Both thumbs up!
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This book has in-depth info on some of the topics that get less attention than they deserve in other physics texts, such as integral equations and hilbert space. The section on tensors is one of the clearest I’ve ever read.
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This book introduces the reader to the basic mathematical structures of theoretical physics: mainly Quantum Mechanics, Electromagnetic Theory, And Classical Mechanics. I used this at UC San Diego for a year long graduate course on Mathematical methods in physics and engineering. If one has the time, there is really a lot to be gained by carefully studying this book. A big part of the book is geared toward developing in detail the mathematics of the Quantum Theory. This is a good thing because in my experience most QM books are too eager to “get to the physics”. It is true that you can get by with a superficial understanding of functional analysis and still do QM, but this book will give you an immensely deeper understanding of the underlying structure of the theory. In particular, the treatment of Green’s functions and integral equations is good. There is chapter on Group Theory and it’s uses in QM. Also is a chapter on Complex analysis, although it is a wise idea to read a book entirely devoted to this subject. Overall, I like this book very much.
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This book was my very first introduction to mathematical physics; in fact, it was really my first introduction to either physics or math beyond the algebra level. At the time I bought it, when I was 9, the vast majority of the book was way, way, way above my head, but that did not stop me from reading it more and more, trying the best I could to make sense of it. I think it is a true testimony to the greatness of this set that it could hold the attention of someone who had no comprehension of about 90% of the material. In the course of almost eight years, I was inspired by this book to get material on calculus, first basic but then advanced, followed by many books on physics. It was largely because of these studies that I started college at 15, and again largely because of these studies that I am now getting A’s in quantum field theory eight years later. I do not bring up these facts of my existance to impress people; if that were my intent, I would be ashamed to write this review. My intent is to give people an example which to some extent gives a slight indication of how wonderful this book is; I only hope that others enjoy this text as much as I do.
Personal stories aside, perhaps I should talk about specific details of this book. Every chapter is excellent, but I feel that some of them deserve special mention: chapters 5, 6, and 7. Chapter 5 is absolutely perfect, and contains a presentation of Hilbert spaces that is hard to find elsewhere. It is very unified, especially in its treatment of Sturm-Louiville polynomials; in other texts, the principal members of this set are given individual treatment, with little or no sense of unification, but here, the enlightening knowledge is revealed that they are all really the same thing, but with different weight functions. Chapter six is a fine treatment of analytic function theory, with special emphasis on the unifying Cauchy-Goursat theorem, and a precise discussion on which theorems imply others, what are the particularly strong results, and what are the most valuable techniques for the practising physicist in this vast field. Chapter 7 is an excellent introduction to Green’s function theory, with special emphasis on the fact that the Green’s function is not only determined by the differential equation, but also, and very importantly, by the boudary conditions. There are many other wonderful things about this book, but to express them all, I would have to write a book myself.
Rating
If you are like so me, you have spent years torturing yourself with horrific books like Matthews and Walker or Arfken. But almost by accident I came across this absolute gem, this masterpiece of balance between rigor and informality. The book presents mathematical physics on a level that is exactly at the level of graduate physics. The notation, the viewpoint and the emphasis are exactly what you need to master just about all the mathematics in graduate physics. This is all done not as Afken or Matthews and Walker do it, by slapping together hodgepodges of this and that into a cookbook, but by unifying mathematical physics into a beautiful tapestry, with the underlying fabric of linear vector spaces.
This book would be worth it if the price were 10 times more than it is.
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If you’re tired of reading descriptive physics like Paul Davies’ books and want to be able to read the original papers and follow the math, this is the book. It presumes a strong undergraduate math background in some areas but the explanations are clear and the proofs are easy to follow. If you want to read quantum physics, the chapters on vectors and operators will give you the math foundations.
Rating
This book gives an excellent coverage of mathematical physics from the standpoint of a vector space. It takes all of the mathematics that would normally be spread out over many courses and brings it together in one book. The treatment given here is concise and complete. It is well written and easy to follow unlike some texts.
As other reviewers have said, this book is for advanced students. People with a strong mathematical background should gain a lot from this book. Undergraduates would probably find most of this book too hard. However, because this book is so good, undergraduates with an interest in mathematical physics could also gain a lot from this book.
Coming from Dover this book is not only very good, it is very cheap, which makes it extremely good value. I highly recommend it.
Rating
The first chapter on vector analysis from the component view is the best treatment of the subject I’ve seen anywhere. I worked through it and the subsequent chapters on linear algebra before going to college, and it literally doubled or tripled my mathematical confidence/ability.
Now that i’ve had some more physics, i’ve been going through some of the other chapters. The treatment of each subject is framed in a way that makes immediate application to physics natural and intuitive. However, while the level of rigor falls somewhat short of many pure math analysis textbooks (ex: lebesque integration is discussed qualitatively, whereas ideally one would have studied measure theory and lebesque integration before hilbert spaces and other topics), the author does a good job of giving appropriate mathematical caveats this book (in my opinion) strikes an excellent balance of practicality without sacrificing rigor. I think this makes the book useful for physicists who would like a rigorous intro to the math without getting bogged down in (relatively) unappliable mathematical constructs.
Overall, this book is a must. I’d recommend the book early (as soon as one’s taken multivariable calculus). There won’t be any math in any physics course that you won’t feel comfortable with after you’ve read through this book.
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One should buy this book just because of the way Green functions are explained. I wish I had had this book during my studies. It would have made things much clearer…
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This is a great book, esp. at the price; but it is going on for forty years old, and it is showing its age: theoretical physics once looked like this, and maybe it still does for undergraduates, but the content does not correspond, or even really give you a proper idea of what you can expect these days in theoretical (and particularly mathematical) physics at research level: no differential manifolds, no Lie groups, no differential forms, no algebraic topology, no symplectic geometry, and certainly no clifford algebras (! – yeah, I know, the last is unfair).
It’s still great, and you should buy it, esp. at the ridiculous price, but you are going to have to read other stuff as well, and the other stuff will look a lot less like what you learned in school.