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Good book for First Course in Calculus based Classical Mechanics

  1. Jun 21, 2014 #1
    I have taken a look at Kleppner and Kolenkow and that seems around the right level of difficulty but I was wondering if there were any other books that worked well alongside the Walter Lewin lectures on OCW. Would K&K?

    Also, where does K&K go up to? Does it include all undergraduate Classical Mechanics or just 1/2nd year? Could you go from this to say a graduate text?

    I am looking for general feedback for K&K but also recommendations of books that I could use and could you please tell me which books are lower or upper level and if they cover all undergrad material. Finally, is Taylor's book appropriate for undergrad or just lower or just upper level? If it's upper level, could you use K&K before, if K&K is lower level(?). I am sorry for the unorganised nature but I am just trying to get a better picture of what approaches I could take.
     
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  3. Jun 21, 2014 #2

    verty

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    MIT OCW has a course 8.012 that uses K&K, there are lecture notes and assignments. And if you look at the calendar for 8.01 and 8.012, you can perhaps see how they compare. K&K is regarded as a difficult book because it uses calculus throughout and has derivations in lieu of explanations. But if one knows calculus very well, the math is a language that explains better than words can.

    The closest book to the first Walter Lewin course would almost certainly be Newtonian Mechanics by French, I think he was a previous teacher of that subject. Professor Lewin uses some of his materials in the videos, usually diagrams for the overhead.

    I don't know enough to answer your other questions.
     
  4. Jun 21, 2014 #3
    That 8.012 course actually looks good. However, there are only a few lectures. I also notice that it misses out some topics in K&K such as relativistic kinematics. Would you suggest I just complete K&K without Lewin lectures or with? Would K&K alone be enough to then study some electromagnetism i.e. Purcell? Thanks.
     
  5. Jun 22, 2014 #4

    verty

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    Oh sorry, I didn't realise there weren't lecture notes for that course, usually the notes are pretty good, as good as the videos.

    Definitely with the Lewin lectures, I think they are very entertaining.

    K&K should be enough, you could always ask questions if something is not making sense. It does progressively use more and more calculus, for example eventually using multiple integrals for center of mass, as well as Stokes' theorem. This is all math needed for Purcell anyway so I think it is good to see it early. I believe the authors intended their book to be usable by students who are learning multivariable calculus at the same time.

    If there is any difficulty, I expect it to be with this multivariable calculus. But my advice there is to remember that it is just an extension of calculus to multiple dimensions, everything has its higher-dimensional analogue. The tangent, the gradient, they are all present and work in similar ways, so thinking "how does this compare to the single-variable case" is, I believe, the right way to learn it.

    I don't think K&K is as difficult as it'll look to many people, it is supposed to be an easier way to learn by using more advanced math to be more accurate. I think you could definitely proceed to Purcell afterwards, you would have used some of the math already and should be well prepared.

    To go further with mechanics, you would need a Lagrangian/Hamiltonian book. This is not a topic I know much about except that it is difficult. Taylor's book seems to be half revision/half new content, probably there would be some overlap with K&K, there is probably a more direct path.

    I suppose it can't hurt to give a possible book:

    https://www.amazon.com/Calculus-Var...426919&sr=8-3&keywords=calculus+of+variations.
     
    Last edited by a moderator: May 6, 2017
  6. Jun 22, 2014 #5
    Thanks a lot. I will go with K&K with Lewin. As far as multivariable calculus, that is no problem because I am currently working through Hubbards book.

    As for Langrangian mechanics, I have a book I bought by accident by Kibble and Berkshire that is meant for upper level courses I think and includes such topics so I can use that when I am ready.
     
    Last edited by a moderator: May 6, 2017
  7. Jun 22, 2014 #6

    verty

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    How is that Hubbard book by the way? Does it have good exercises? By good I mean, are they helpful for understanding?

    (I did some editing here to make the language better)
     
  8. Jun 22, 2014 #7
    I think it is brilliant. There are plenty of exercises at the end of each chapter and they greatly helped my understanding. It is also written in a very inspiring and motivating way I found that makes you interested in constantly advancing to the next exercise or page. Highly recommended!
     
  9. Jun 22, 2014 #8

    verty

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    Oh right, so it's actually a good book. I thought any book with "differential forms" in the title wouldn't be good. It just goes to show, there are many books out there and there are many variations on a theme. It's amazing how many different books and styles there can be for a single subject. In a way it's and in a way it's bad. All books should be the same, it would be easier (in the sense that too much choice can be debilitating).
     
    Last edited: Jun 22, 2014
  10. Jun 22, 2014 #9
    I agree that they should be organised and labeled in some way as well. However, I am sorry if I am sounding naive but what is wrong with "differential forms"? It's just multivariable calculus free of a co-ordinate system isn't it? I think it's seen as a more rigorous approach(?).
     
  11. Jun 22, 2014 #10
    With all I have praised it, it is worth bearing in mind that I am self studying it without the aid of an instructor and I feel this book is great for that. I have read that it can be a bit slow otherwise(?) and that Spivak is a better option. However, I was under the impression that Spivak did not include as much and wasn't suitable for a multivariable calculus course. Do you know if this is correct?
     
  12. Jun 22, 2014 #11

    verty

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    I know absolutely nothing about Spivak's manifolds book. I know he wrote that and 5 volumes of differential geometry, so clearly that is his speciality.

    I wouldn't say that differential forms are a more rigorous approach, I mean I don't know that much about them but it looks to me like a more concise notation. But I don't know about pullback and all that, I suppose there must be some elegance to it. But let's take Hubbard's book for example. I grant you that it is a good book about differential forms, but the title suggests it is for vector calculus and linear algebra only. Both of those are pretty elementary subjects. So if one is learning these forms just to be able to do the same old same old, then any such book should be a more difficult way to learn.

    This was my thinking. And I wondered about the exercises, if they reduced the difficulty of the material. But I believe you that they do. So it's another book on the pile of books for multivariable calculus. There are ones called "Advanced Calculus", ones called "Multivariable Calculus", ones called "Vector Calculus", ones called "Vector Analysis", ones called "Calculus of Several Variables". And ones called "Calculus", like Courant and Apostol. It's amazing how many books there are, is all.

    Something different now. I seem to remember but I can't confirm it by searching, either the old threads are gone or it was someone else. But I seem to remember that you were someone who bought University Physics. And now you are asking about K&K, but these books obviously do overlap. So I just thought if it was you, perhaps you thought K&K was at a higher level, whereas I don't think it is necessarily, it just uses calculus more openly from the start and has some more detailed derivations. But you could learn mechanics from the other book as well.

    Or I could be mistaken and it was somebody else.

    Edit: I'm starting to realise that maybe Hubbard intended his book to be just another multivariable book, but using this new notation. So actually in that case it won't be what I thought, a kind of second book on the subject. So actually, it probably is pretty good because it makes it quicker to learn this new notation. So I think I was on another page entirely.
     
  13. Jun 22, 2014 #12

    verty

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    I'll write this here to so that I can link to it in future. With regard to K&K versus a book like University Physics, it is important to make a distinction between the language of a book and the subject of a book. The language of a book is what level of math it uses. The math is part of the language used to describe the subject of the book. So a graduate book will used more advanced language because the reader knows more advanced math.

    The subject of a book is what the book is trying to teach you. So with these two books, both have been used at MIT, both (as far as Newtonian mechanics goes) are trying to teach you the same things, the subject is the same. The language is slightly different because K&K uses calculus very openly. UP also does but it can be skipped because it is meant for high school students now entering college. So it is slower going but does include some derivations and does include some calculus problems.

    So by this categorization, the subject is the same but the language is slightly different, but I would say not different enough to need both. UP covers relativity even, it really does overlap almost entirely with K&K. And this is true with VERY MANY books. On any one subject there are way many books, but usually most of the difference is language, they will generally teach the same topics although some will go further or into more detail. But there is really no perfect book, there are just books that use language that you understand and teach what you want to learn, and beyond that it is down to effort and dedication to work through them.

    And of course we can judge books by how well they enable one to self-study. By this standard, the Hubbards book mentioned earlier sounds good indeed. The language of that book may be at a higher level but it is another multivariable book, it'll teach that subject along with some new notation. Hence why I lament the number of books, there really should be fewer.

    That is all.
     
  14. Jun 22, 2014 #13
    I don't think that was me. I considered University Physic sat one point and I may have spoken out of context but I don't think even that - I had a look at past posts to see if I spoke out of context.

    Yes, there are a lot of such books. I did look around quite a bit though and this definitely seems to be the best and most comprehensive book on multivariable calculus, even if it has a few minor flaws. Which books don't?

    Having a look at later chapters, it goes into a number of forms topics in Chapter 6. I think that Hubbard is also quite versatile in that a variety of people can use it. If you want a rigorous treatment you can use the appendixes at the end that delve into "harder proofs", as he puts it, so I think it will be quite useful for someone wanting a book like Spivak, like myself. I actually mentioned this on the textbook listing thread for this book.
     
  15. Jun 22, 2014 #14
    Interesting, so would you want fewer books at the same level or just fewer levels of depth for a subject. Sorry, if that make little sense and I have misunderstood you.
     
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