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Classical Spivak's Physics for Mathematicians: Mechanics

  1. Aug 10, 2016 #1
    I will be enrolling in an undergraduate Classical Mechanics course and I was wondering if the book by Spivak "Physics for Mathematicians: Mechanics" would help me understand the concepts more in depth than usual.
    Until the time that I will be taking the course, I will already have finished undergraduate course in General Relativity and Theoretical physics(separately). So, I think that I will have some knowledge of some of the concepts that are presented in this book; my background in mathematics will be a little bit more advanced than the rest of the students that will be taking the course.
    Thanks in advance.

    P.S. If anybody has used it or read it a little bit, what are your opinions?
  2. jcsd
  3. Aug 11, 2016 #2


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  4. Aug 11, 2016 #3
  5. Aug 11, 2016 #4
    I own the book and have read parts of it. I do not like it at all. It is very confusing, and a lot of it is unhelpful. For example, his first chapter discusses Newton's principia, which is notoriously difficult to understand. I don't understand why he takes so much time in discussing this book. Of course, if you're interested in the historical context, then this book might be helpful to you. Otherwise, I suggest you study classical mechanics from books written by physicists. Even for mathematicians, there are a lot of good alternatives such as Arnold or Marsden.
  6. Aug 11, 2016 #5
    Do you think that these books-which are intended for mathematics students-would be helpful for me during a first course in Classical Mechanics?
  7. Aug 11, 2016 #6
    What do you mean with a first course in classical mechanics? How can you already have taken GR and theoretical physics without any knowledge of classical mechanics? What is the contents of the course?
  8. Aug 11, 2016 #7
    Well, it's a complicated story, but I am self-studying everything that those courses have as prerequisites so I can successfully complete them.
    The contents of the courses are the standard material that every university that teaches their undergraduates general relativity and theoretical physics contain.
  9. Aug 11, 2016 #8
    Maybe it would be more helpful if you gave a list of things in classical mechanics you know (for example, you might already know kinematics and Newton's law), and the content of the course you'll take.
  10. Aug 11, 2016 #9
    Well, I will be self-studying some part before I take the aforementioned courses(I have not taken any of them yet). I will self-study Lagrangian Mechanics(from Morin's book). Other than that, I just know about Newtonian Mechanics, but nothing fancier than first-year undergrad material.
    The Classical Mechanics course's contents are(from a rough translation of the syllabus):
    -Inertial reference frames and generalized coordinates
    -Newtonian Mechanics
    -Linear and non-linear oscillations
    -Lagrangian formalism
    -Calculus of variations
    -Central potentials
    -Gravity fields
    -Conservation laws
    -Oscillations of small magnitude
    -Mechanics of rigid bodies
    -Hamiltonian formalism
    -Noether's theorem and symmetries
  11. Aug 11, 2016 #10
    Last edited by a moderator: May 8, 2017
  12. Aug 11, 2016 #11
    Yeah, Taylor is great, I just borrowed it from the university library. But, as I will already have some knowledge of higher mathematics, won't the book by Spivak(or Marsden's or Arnold's book on Classical Mechanics) help me go deeper into the subject?
    Last edited by a moderator: May 8, 2017
  13. Aug 11, 2016 #12
    @micromass Also, how can I PM you about something relating self-studying of mathematics?
  14. Aug 11, 2016 #13
    Sure, but books like Taylor have a very different goal and scope than Arnold or Marsden.
  15. Aug 11, 2016 #14
    If I use Taylor and supplement it with one of those books so as to gain a deeper understanding of the differential geometry that's behind classical mechanics?
  16. Aug 11, 2016 #15
    That would be an excellent thing to do!
    Feel free to PM me any time!
  17. Aug 11, 2016 #16
    The funny thing is that I can't find how to PM a user!
  18. Aug 11, 2016 #17
    Click on username and then "start a conversation"
  19. Aug 11, 2016 #18
    @micromass One last thing: Which of these books would you suggest for me to supplement Taylor's?
    1) Marsden's
    2) Arnold's
    3) Spivak
    4) Other
  20. Aug 11, 2016 #19
    I would go for Marsden. Spivak is very confusing and I don't like his treatment. Arnold might be too advanced however and while Arnold does treat differential geometry, if you haven't seen it before, then Arnold's treatment is not enough.
  21. Aug 11, 2016 #20
    Aren't Morin and Taylor roughly equivalent? (With the possible exception that Morin has a large number of problems with solutions.)
  22. Aug 11, 2016 #21
    Not really. The books are very different. They are meant for very different audiences too.
  23. Aug 12, 2016 #22
    I think that using both of them will be ideal!
  24. Aug 12, 2016 #23


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    I was a little curious to see how another book on physics could be written by a mathematician. [Mathematicians started writing serious books on physics in 1918, with the famous "Raum, Zeit, Materie" by Hermann Weyl and have been doing that quite a lot ever since. It's worth mentioning the 2nd (from a chronological perspective) cornerstone of the literature on Quantum Mechanics, the "Mathematische Grundlagen der Quantenmechanik" by John von Neumann (1932)].

    Actually, it was not a bad writing by Spivak, au contraire. A little under 700 pages is a lot of material for the reader/student, but remarkable books take many pages to write, no doubt (incidentally, the only exception I could mention is also in the field of classical mechanics, the gem by Lev Landau and Evghenii Lifschitz). The source of inspiration for the author appears to me to be given by classical (i.e. pre-1950) books, of which I mention the book by W.H. Osgood ("Classical Mechnics", 1st Ed. 1937). This book, though mathematical in nature, has a double advantage compared to, let's say, Goldstein or Morin+Taylor or Marion+Thornton:
    - Puts emphasis on the long history of the topic, starts off with a careful (perhaps boring) analysis of Newton's thinking. Never leaves historical notes, sending the reader to the bibliographical items containing original material from the golden years of CM in the 19th century.
    - Is mathematically accurate and balances this rigor with the descriptive style needed by a physics book, especially in mechanics.

    Spivak's work is necessary, because it's the missing step in the overall literature on this important topic between the frightening (to me, at least) books by Arnold and Abraham+Marsden and the plethora of purely physics books of which I mentioned 4 in the previous paragraph. The only real question is: how relevant is the study of this book for someone wanting to go all the way in physics? This is judged only by the real interest of the targeted reader: aiming to become a mathematical physicist, for which I believe it to be helpful. Using the methods of differential geometry in the study of classical mechanics - gently presented in this book - prepares the reader for the thorough study of General Relativity under the guidance of R. Wald and Hawking+Ellis, or prepares him for a deep understanding of gauge field theory.
  25. Aug 12, 2016 #24
    Well, I want to become a theoretical physicist, so I think that books like this can only do some good.
    Did you read the book? Is it well-written?
  26. Aug 12, 2016 #25


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    Micromass criticized it, but I liked what I read, including the historical context. I couldn't have gone through all of it for the lack of time, of course. I recommend it as an alternative to a classical physics one,
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