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Recommend me some textbooks for self study

  1. Aug 27, 2006 #1
    OK, I want to self study classical EM in greater depth than my electromagnetics course, and I plan on working through Jackson (I am currently an undergrad). I want to get into the relativistic treatment of the subject. However, to properly tackle this, I feel my mathematics background is lacking.

    I have of course had u. phys 1 and 2, and electromagnetics (textbook I used was elements of electromagnetics by N.O Sadiku). The mathematics I have had includes, calc 1, calc 2, calc 3, diffEQ, Adv. eng math (complex analysis), and prob/stats. I, surprisingly, have never taken a linear algebra course.

    So, that brings me to my next point. Before I finally take a linear alg course, what book would you recommend for self study in linear alg?

    Also, I want to self study tensor analysis. What book would you recommend for this?

    I also would like another go around in vector analysis, just to make sure I know the subject like the back of my hand. I have already studied the subject from Stewart's calculus. What book would you recommend for a more in depth treatment of the subject?

    Are there any other fields of mathematics I should self study? After tackling classical E&M I would like to self study relativity (beyond what is introduced in Jackson), Quantum Mechanics, QED, and finally QFT, all at the ugrad level. What mathematics should I be comfortable with to properly tackle these subjects.
     
  2. jcsd
  3. Aug 27, 2006 #2
    I can't imagine doing any kind of math, science, or engineering without any linear algebra at all. Linear algebra is definitely a strong prerequisite for any kind of advanced vector analysis as well as essentially any higher subjects (including E&M)

    As for relativity, I've been reading Carroll's general relativity notes (I'm going to buy the book soon) as well as Hartle's GR book. They mesh quite well together. On top of this I've been recommended the Schaum's outlines Tensor Analysis to cover the tensor stuff that is necessary for GR, but I don't own that one.

    I've been reading Jackson also and my only pick is that he assumes knowledge and skill at a strong level already (as rightly he should) My prof suggested I read and fully understand all of griffiths first.

    I'm interested in what other people have to say also since I'm going to buy a bunch soon also.
     
  4. Aug 27, 2006 #3
    Ugh, bunch of answers:

    1st, I think Jackson is a little too much as an undergrad, at least I can't handle it yet, maybe you can.

    2nd, For self study of Linear Algebra I'd recommend Axler's Linear Algebra Done Right. As a lighter reading, and maybe with more applications if you lean towards engineering, you could go for Anton's Introduction to Linear Algebra.

    3rd, I'm currently learning Tensor Analysis from some notes the professor gave us, so I really can't recommend a book from first hand experience.

    4th, Vector Analysis? Hmmm, there's Spiegel's book in the Schaum's series, but I also like Vector Analysis by Hwei Hsu.

    5th, If you have some spare time a read through a more in depth Calculus book, like Apostol's, is completely worth it. Also, a book on mathematical methods for physicists might be useful, I like studying from both Arfken and Boas. If you think you mastered "classic" calculus, you can go a step further and introduce yourself to some Analysis books, Rudin's and Pugh's are the ones I use, Rudin's is expensive though, try to get it from the university library.

    Good luck!
     
  5. Aug 27, 2006 #4
    Well, even in my EE curriculum, linear alg. is not a requirement at all. All of the linear alg used in my engineering classes is kinda covered on an ad hoc basis. Now, the physics degree requires linear alg, but the only class it is a pre-req for is QM.
     
  6. Aug 27, 2006 #5
    What text are they using? Typical textbooks are Hoffman & Kunze and
    Strang but the Schaum's outline might be better for self-study.

    A book that covers linear algebra with a focus on what's needed for QM
    is Byron & Fuller, Mathematics of Classical and Quantum
    Physics
    , but it may be a little too sophisticated for a first
    introduction. Lots of yummy math in here, though.
     
  7. Aug 27, 2006 #6
    For some reason the forum is rejecting my posts, so I had to break up my reply. In particular, it seems to have something against

    Div
    Grad
    Curl
    And
    All
    That

    being on a single line (seriously). I haven't read this book, but it's popular.

    Studying more E&M will exercise your vector calc pretty well. My
    favorite book on E&M is Schwartz, Principles of
    Electrodynamics
    . This does introduce some relativity, but using
    the old "ict" method to make the metric Euclidean. So you'll still
    need a more modern introduction to SR. Rather than introduce the
    covariant Maxwell equations as an afterthought, Schwartz first covers
    electrostatics and SR, then "derives" the full Maxwell equations using
    Lorentz covariance as a guide. He reviews vector calc at the
    beginning and introduces enough tensor algebra for an understanding of
    the Faraday and electromagnetic stress tensors. His coverage of
    radiation, diffraction, and wave guides are just as lucid and
    inspiring. It's a beautiful little book (a little over 300 pages),
    and a very enjoyable read from cover to cover. One of the best
    technical books ever written IMO.

    Tensor calculus it is probably more fun to pick that up from an
    introductory General Relativity text like Schutz, A First Course in
    General Relativity
    . There's also a pretty good Schaum's outline
    on tensors.

    My undergraduate QM text was Gasioriwicz; great text, but not good for
    self study. For review, I just ordered the inexpensive little book
    Primer of Quantum Mechanics based on the Amazon reviews. I've
    also heard great things about Shankar.

    For SR, my favorite books are Spacetime Physics -- which covers
    just the basics, but very thoroughly -- and Rindler's Relativity:
    Special, General, and Cosmological
    . And the previously mentioned
    Schutz does a good job with SR, too.

    For QED/QFT at the undergraduate level, a new edition of Griffiths
    particle physics book is coming out soon. I think the books by
    Aitchison & Hey are at about the same level or a little higher.
     
  8. Aug 28, 2006 #7
    That's funny because when I was an undergrad, Linear Alg was not required. But, I found out that it helps tremendously when I took QM. I think your prof is right suggesting Griffiths' book. That book is written very well. When I took E&M as an undergrad, my prof made us use Jackson as a reference. The problem is I had a hard time understanding it. So, I didn't end up using it very much at the time.
     
  9. Aug 28, 2006 #8
    Okay. Some partial differential equations would help if you're going to attack Jackson. You probably learned the meat of what you need to know from your undergraduate (presumably Griffiths-level) E&M course, so you may or may not need to dig too deeply into the formalism. The first thing that will be mathematically more advanced in Jackson's text is the introduction of Green's functions. In E&M you can think of Green's functions as the potential from a point source, from which you can build up the potential of a charge distribution. In math, they are the solutions to PDEs that prodce delta functions. In QFT they are the propagators that tell you how a particle travels from one point in spacetime to another. They're pretty important--I'm not sure if a formal study of them from a mathematical point of view is necessary, but it couldn't hurt.

    I should also warn you that there are a lot of details in Jackson that aren't necessarily prerequisite for the course of study you're proposing. In fact, you might want to intersperse a little bit of advanced mechanics in your self study. It helps to see the Lagrangian and Hamiltonian formalism of a classical field theory and how to manipulate some slightly more formal things, such as poisson brackets and such. (And if you can geometrically quantize a classical field theory into a quantum field theory, you're automatically a rockstar in my book.) Some recommendations: Marion/Thornton will do the trick, though if you really like the subject, you might want to dabble with some of Arnold's Mathematical Methods of Classical Mechanics (the latter is somewhat advanced for physics students).

    You're probably not missing too much. You learn a lot of linear algebra in quantum mechanics, but conversely quantum mechanics is a piece of cake if you have a strong linear algebra background. A basic introduction can be found in Bretscher's text. A more advanced text is Apostol (which I think is multivariable calculus/linear algebra in a unified approach). I believe the latter talks about some more formal things for quantum mechanics ("hermitian operators" or "self adjoint operators" are the key words that you want to look into when studying sections).

    Tensor analysis is usually first introduced to physicists in general relativity (GR). You'll pick up some in Jackson. You might want to try to read the first few chapters of Sean Carroll's GR book. Or find the GR book which 'speaks' to you. (Everyone has their own ideal textbook.) You can look into D'Invierno, Schwarz, or even Misner Thorne Wheeler (if you're really perverse and like antequated language).

    Maybe the Apostol book mentioned above. But hey, you'll learn/review more vector calculus by going through Jackson and making sure you understand every step and do problems. I wouldn't recommend spending too much time reviewing vector analysis math textbooks unless you feel particularly weak in certain topics.

    You mentioned you had complex analysis, so that's very good (you don't really use it until QFT and it can sneak up on you if you're lazy). You should also have a good background in fourier analysis. This is usually taught in a PDE course, though some schools have separate fourier analysis courses. I have no good textbooks to recommend to learn this. You learned some in Griffiths. The only PDE book I'm really familiar with is Stewart, which I didn't think was particularly illuminating (but it will teach you about Green's functions and fourier transforms). Perhaps a mathematical physics book (Boas or Arfken).

    For Quantum Mechanics the standard "first book" is Griffiths. It's exceptionally clear and well written. You'll want to go a little more advanced than this, however, and Shankar is very good for self-study. This will get you caught up to just about graduate-level quantum. There are other 'classic' texts to read select topics from: Sakurai, Schiff, Merzbacher. But don't get too bogged down going through entire chapters that you've read in other texts already.

    For quantum field theory, first read a particle physics book such as Griffiths' Elementary Particles or Halzen & Martin or Perkins. Learn how to calculate Feynman diagrams, even if it's somewhat mysterious at the time. I would then suggest a combination of the pink oxford press book ("A Modern Introduction to QFT" or something like that) and Zee's Quantum Field Theory in a Nutshell. After this, you can easily graduate to texts such as Greiner (Field Quantization, Quantum Electrodynamics) and Peskin & Schroeder.

    Best of luck with your self study.
    -F
     
  10. Aug 28, 2006 #9
    Sorry to pick on a single line from a long post, but what exactly do you find antiquated about MTW?
     
  11. Aug 28, 2006 #10
    This is a very good point. It reminds me that I saw this amusingly titled book in a bookstore:

    [​IMG]
     
  12. Aug 28, 2006 #11
    LMAO!!! :rofl:
     
  13. Aug 28, 2006 #12

    Thank you for the excellent advice!
     
  14. Aug 28, 2006 #13
    Hehe, maybe I'm being a little biased. I don't have a copy of MTW handy, so part of all of the following may be rubbish. For one the notation is a bit old (don't they use "div" "grad" and "curl" instead of the nabla operators?). If I recall correctly, they also use excessively script-y letters that are difficult to write down when one is taking notes. (Weinberg seems to have the same ailment in his QFT books.)

    Also, the approach (while novel) is orthogonal to anything else currently being used. This doesn't make it worse--but I found it difficult to get anything out of it when I was looking things up to cross reference with Carroll (which was my main reference). However, if one is reading Carroll, one can simultaneously reference Hartle (a little easier), Schutz (whom I misspelled in my last post), D'Invierno without too much trouble translating between them.

    My take on the text was that MTW approached GR from the point of view that physicists don't know any differential geometry, so they should be taught a cartoon version of differential geometry as they learn about GR. By "cartoon" I mean references to one-forms as little pac-man like objects that "eat" vectors and other graphical representations that are mathematically accurate, though a little silly. I think of it this way: MTW explains things at the level and detail of a professor talking to a confused student in office hours. They go into lots of detail about developing an intuition for the mathematical machinery. Again, this is not a bad thing. In fact, it's a terrific thing. But...

    More modern texts (D'Invierno and Carroll in particular) are a little more formal in their approach. They go ahead and explain covariant and contravariant tensors in terms of how they contract with other objects and how they transform. As a result, they're a lot shorter. (In fact, Carroll, D'invierno, and Shutz probably take up less volume on one's bookshelf than MTW.) I thought it was very nice to be able to look at a section title X and then say, "gee whiz, I'm confused about X... let me look up X in this other [modern] book." And when one looks up that topic in another book, one can be assured that the general approach (i.e. what you are expected to know up to that point in the book) is about the same.

    Also, if one already has some background in differential geometry (apparently something anomalous for physics students in the MTW era), reading through MTW can be excruciatingly slow (not without illumination, though).

    Anyway, I didn't mean to bash MTW... if one can get into it, then all the more power to him/her. I have found, however, that it's not as useful as a reference when one is learning the subject for the first time (a) with some differential geometry background and/or (b) in conjunction with other texts.

    By the way, the coloring book looks fantastic!

    -F
     
  15. Aug 28, 2006 #14
    Actually, I would characterize Carroll's approach to Riemannian geometry as "classical", and less "modern" than MTW. I would agree that MTW tends to go off on tangents while Carroll is much more focused. I think the heuristic and geometric methods used in MTW are still useful.

    Yeah, but kind of pricy for a coloring book!
     
  16. Aug 28, 2006 #15
    would you say that the presentation of differential geometry in MTW is a good one? or is it far better to work with a seperate differential geometry text?
     
  17. Aug 29, 2006 #16
    In the math curriculum, differential geometry at the undergraduate level covers the local and global theory of curves and surfaces (or maybe just the local theory if time is limited), with maybe a touch of Riemannian geometry at the end (i.e. generalizing the theory of surfaces), and then Riemannian geometry is covered fully in a grad course. Do Carmo, for example, has two books Differential Geometry of Curves and Surfaces and the "sequel" Riemannian Geometry. A good library will probably have those. The chapters on local theory will be the most relevant. (I actually took a grad course in Riemannian geometry out of the Do Carmo book before having any exposure to undergraduate geometry. I found the text very readable, but some of the problems assume you know the material of the first book.)

    Some other undergraduate texts are O'Neill (who goes beyond the classical approach and introduces differential forms), Milman & Parker, and Pressley. There's even a pretty good Schaum's outline.

    The typical GR book, including MTW, covers just Riemannian geometry (Carroll does this very well, BTW), and not the local theory of curves and surfaces. And rightly so as it's out of the way, and they want to get to the physics as quickly as possible. I do think you miss out on building some intuition that way, though.
     
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