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Almost done with 1st year of physics, doing really well, but

  1. Mar 26, 2012 #1
    I'm pretty confused at the moment. I am doing great in my first year of calc-based physics, and when I read the text (I finished it before I even took the course lol), it was hard, but I plowed my way through and in the end looking back I thoroughly enjoyed it. That's also why I'm probably doing so well: it's low pressure when you've read the text in its entirety and have understood most of it before even stepping into class day 1 of the term. However I'm taking a look at the advanced physics texts, and I am just not excited about them. Compared to first year physics, there is a gargantuan jump in depth and difficulty. Not just in the jumbles of equations and symbols (stuff that would be cured by taking the requisite math methods courses) but in the formalism, logic, and description in the texts. Teaching myself this material is like pulling teeth (e.g. Marion and Thornton). So my main question is: why do I hate this stuff?

    Is it A) because I am trying to learn the wrong way by teaching myself something that you really can't learn on your own (unless you are a genius), and I should wait and see how I feel during advanced physics courses with a live professor before I judge whether this is for me?

    Or B) would I be bored and not interested even if I acted like a normal student and didn't feel the compulsive need to teach myself all of the material before taking the course (an OCD based on fear of failure, for those who were wondering), and my lack of enthusiasm for the upper level stuff is simply indicative that physics beyond the first year just isn't for me?

    Thanks for any help you can provide.
     
  2. jcsd
  3. Mar 26, 2012 #2
    I think in response to this I would like to ask a question, and maybe that will start a useful conversation.
    So, here it goes :-)

    How much vector calculus do you know?
     
  4. Mar 26, 2012 #3
    not much - i haven't taken the math methods course yet - that's supposed to be this fall. the multivariable course i took which is a prereq for math methods only did a little intro vector calc, not the meat and potatoes.
     
  5. Mar 26, 2012 #4
    It doesn't take a genius to teach yourself Calc-based Physics II-- but it does need a certain mind-set. What you need to do is try to think of it in different ways. In physics II (abbreviating for calc based physics II), the equations start to be more heavily dependent on context and meaning. That is, your not just reading letters-- you should try to understand the equation conceptually. The first topic that you are introduced to is electromagnetic fields. Is that what your having trouble with?
     
  6. Mar 26, 2012 #5

    jtbell

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    Staff: Mentor

    His reference to Marion and Thornton (a common upper-division classical mechanics text) suggests that he's looking beyond the Physics II level.

    Back to the OP: upper-level textbooks do usually demand more from students. They tend to have fewer worked-out examples and pretty diagrams, and do a lot less "hand-holding" in the way of filling in all the steps of derivations. It's not impossible to self-learn from them, but you have to work through them carefully, treating gaps in derivations as exercises for you to solve, etc.
     
    Last edited: Mar 26, 2012
  7. Mar 26, 2012 #6
    To make things easier for you , you should study vector calculus and most importantly vector calculus in curvilinear co-ordinates then classical mechanics will be easy for you . Take a look at Taylor's classical mechanics he covers the mathematical prerequisites well. You can also try boas mathematical methods , There is a solution manual available in case you get stuck in the excercises .Be careful Marion and thorton is not always easy for beginners try other textbooks instead)
     
  8. Mar 26, 2012 #7
    Can you share the book you are studying from? A solution manual for the respective book can really help. They have one for Thornton/Marion's Classical Dynamics of Particles and Systems, 5th edition if that is your book.
     
  9. Mar 26, 2012 #8
    Thornton and Marion is a truly awful textbook. That's why you don't like it. Take a look at the reviews on Amazon.com. Lots of people hate that book.

    Do they hate it because they aren't smart enough to learn from it? No. Do they need more "hand-holding"?

    Quite the opposite. They are too smart to learn from such a piece of trash. If someone thinks it's a good book, I think they probably don't understand classical mechanics very well.

    It's not about filling the gaps. In order to understand mechanics, you have to do much more than "fill in the gaps" to that book. You would have to entirely rewrite it in a completely different way. Not just fill in gaps. If you just want to be able to simply derive the results with no understanding of the concepts, all you have to do is fill in the gaps. But if you want to have some insight into classical mechanics, that's a totally different story.

    Probably any other textbook would be significantly better and more interesting than that one, but most of the alternatives are probably not that great, either. Arnold's book on CM is good (especially the later chapter), but probably a bit too advanced for that level. Still, it may be worth a look. Lanczos' book is also better than most. Still not the best. Also, Baez's classical mechanics course notes on his webpage are pretty good, but might also be a bit advanced on the whole for that level. Landau and Lifschitz is supposed to be good too, but I haven't read it, and, again, might be too advanced for this level. But, these books might be worth a try.

    Spivak wrote a nice book about mechanics, too, but I only read a small portion of it (which I was very impressed by), so I'm not sure if it's quite what is needed here.

    Penrose's Road to Reality has a very good, but very incomplete and inadequate chapter on Lagrangians and Hamiltonians.

    I am working on my own notes about classical mechanics, designed as a supplement to other textbooks that will cure many of the ills of the present pedagogical disaster in classical mechanics, but they have a long way to go before they are ready.
     
    Last edited: Mar 26, 2012
  10. Mar 26, 2012 #9
    I heard good things about Taylor so maybe I'll check it out. So are you saying that there is basically no great text on CM at the undergrad level? The edition of M&T that I am using is the 4th, for those who asked.
     
  11. Mar 26, 2012 #10
    I don't know what all the textbooks are at that level. I kind of moved on to more advanced texts. Also, I'm a math guy, so more mathematical ones like Arnold were suitable for me. Anything is bound to be better than Marion and Thornton, though.
     
  12. Mar 26, 2012 #11
    The reason why you aren't enjoying reading the more advanced level texts is probably because you aren't comfortable with the math. Dealing with the physics is hard by itself but if you will be learning the math side-by-side that makes things a lot more difficult and IMO is a very bad approach for learning physics. Learning the math before dealing with the physics gives a much better experience. Here's what I think you should do before tackling an advanced level book on Classical Mechanics:

    - Familiarize yourself with basic ODE's. First order separable and second order with constant coefficients will probably be the most useful ones (learn undetermined coefficients).
    - Familiarize yourself with some vectors/vector calculus and working in different coordinate systems.

    This should be enough to get through the first few chapters for a text such as Taylor/M&T (assuming you already know a decent amount of single variable calc).

    For the later chapters you should also know a decent amount of basic linear algebra such as knowing how to diagonalize a matrix (finding eigenvalues and eigenvectors). You should also know Calculus of Variations but Taylor has a pretty good stand-alone chapter on that.

    Once you have the basic math background the physics will seem a lot more understandable.

    As for the best Classical Mechanics text, I'd suggest you work with Taylor's "Classical Mechanics" and supplement it with Morin's "Introduction to Classical Mechanics" for further practice (Morin has several worked out examples at the end of each chapter). Both are very good texts and are extremely readable. This is what I did and ended up enjoying my class greatly and also did quite well.
     
  13. Mar 26, 2012 #12
    thanks - i've been reading boas but stopped at second order ODEs because my semester started and i have less time. i plan on finishing the rest of boas or at least most of it during the summer and with that i will probably be more comfortable with higher level texts. everyone says great things about taylor so thats what i will probably use and cross reference it with M&T because unfortunately thats the text my school uses. what exactly is a curvilinear coordinate system by the way? is that the most generalized version of a coordinate system?
     
  14. Mar 26, 2012 #13
    Oh, I forgot to mention Susskind's classical mechanics lectures. You can find them on Youtube. I think it's pretty appropriate for this level and pretty decent.
     
  15. Mar 27, 2012 #14
    I agree with ahsanxr - the math will probably seem a little unsettling because you haven't had multivariable/vector calculus, linear algebra, or differential equations yet. If you're looking for an intermediary book, I recommend An Introduction to Mechanics by Kleppner and Kolenkow. It covers essentially the same material as a typical Physics I course, but with more mathematics.

    I really enjoyed the classical mechanics textbook by Marion and Thornton. I tried to learn from Taylor, but I found it too conversational for my tastes. But see if your school library has a copy so you can see if it would be more suitable for you. :)
     
  16. Mar 27, 2012 #15

    mathwonk

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    here are some class notes with background for advanced calculus, mostly linear algebra, but some several variables.
     

    Attached Files:

  17. Mar 27, 2012 #16
    Knowing more math isn't going to make Thornton and Marion very much more enlightening. Sure, it will make it easier to understand what they say. But what they say is very shallow conceptually. They prefer mindless calculations to conceptual understanding. By the way, I did very well in the class I took which used Thornton and Marion. The prof was pretty impressed by my performance. That didn't mean I understood the material on a gut level. I was left very unsatisfied, despite understanding the book perfectly well.
     
  18. Mar 27, 2012 #17
    Sounds like it's book list o'clock!

    1. Mathematical Methods in the Physical Sciences - M Boas
    2. Introduction to Linear Algebra - G Strang
    3.1. Mechanics - Landau and Lifgarbagez (Vol. 1 of A Course of Theoretical Physics)
    3.2. Classical Mechanics - Goldstein
    4. Linear Algebra - Hoffman
    First halves of;
    5.1. Modern Quantum Mechanics - Sakurai
    5.2. Non-Relatavistic Quantum Mechanics - Landau and Lifgarbagez (Vol. 3 of A Course of Theoretical Physics)

    Then you should be able familiar enough with stuff to get going

    Oh wait, I forgot E&M and relativity

    6. Introduction to Electrodynamics - Griffiths
    7. Classical Electrodynamics - Jackson (I can't remember if this is the name of it, everyone calls it jackson)
    8. Classical Theory of Fields - Landau and Lifgarbagez (Vol. 2 of A Course of Theoretical Physics)

    Bang and the intro level physics is gone!

    You might want to supplement these with some of the following maths books;
    Calculus - Spivak
    Principles of Mathematical Analysis - Rudin (aka Baby Rudin)
    Introduction to Tensor Analysis and Continuum Mechanics - Heinbockel (it's free http://www.math.odu.edu/~jhh/counter2.html)
    Classical Groups - Weyl
    Spinors - Paul Dirac
    Advanced Calculus - Loomis
    Advanced Linear Algebra - Rome
    Differential Forms, A Compliment to Vector Calculus - Weintraub
    Mathematical Methods - Hassani

    and a bunch of other books, really you should be able to get to a point where you should know what it is you need to know and be able to find relevant books on it anyway so I won't continue this list on forever :p

    Edit;
    Gerard 't Hooft also has a webpage devoted to 'How to become a GOOD theoretical physicist'
    http://www.staff.science.uu.nl/~hooft101/theorist.html

    The main things you want to get under your belt before you head into advanced teritory is
    1. Lagrangian mechanics, action principles and Hamiltonian mechanics (although they are all equivelantly derived from one another)
    2. QM formalism, vector spaces, dirac notation
     
    Last edited: Mar 27, 2012
  19. Mar 27, 2012 #18
    Yeah I would use Taylor to learn from and then just do whatever problems you're assigned from M&T. I never used M&T though since our class used Taylor so I can't comment on its quality. Morin is also a vastly underrated book. I never heard its name a single time until I went around the net looking for problem/solution books. Turns out it's pretty well and uniquely (contains relevant humorous verses) written and is also a great source for practice problems, so consider that book as well. That's the text they use at Harvard's honors freshman mechanics class.

    A curvilinear coordinate system is one where the lines of the constant variables (x,y,r,theta etc) are curved. For example, in a rectangular system, the lines of constant x and y are straight whereas in polar coordinates the lines of constant r are circles (curved/not straight) and constant theta are straight lines.
     
  20. Mar 27, 2012 #19
    Yeah... most people really shouldn't jump from intro level to Goldstein, Landau and Sakurai...
     
  21. Mar 27, 2012 #20
    I don't see why not, if he goes through M Boas' book he'll know all the maths he needs for it and they explain the concepts pretty well. I don't think he'd really be missing anything by going straight to then and he'd be able to derive the things that he'll find simply stated at a lower level himself.
     
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