Spivak's Physics for Mathematicians: Mechanics

[vanhees71]

I am very surprised! I think Arnold's writing is pretty confusing and sloppy. But I didn't think that somebody with your abilities would struggle with it! I always thought Arnold was written with people like you in mind.
If you don't mind, what about Arnold's book weren't you able to grasp? And did you know differential geometry/manifold theory before attempting Arnold?

Uups?!?? If Arnold's book is sloppy, what do you think about the usual physics books then? I thought Arnold is the perfect balance between math rigor and writing in a comprehensible way. Sometimes math is written in so formal a way that I, as a mathematically very interested theoretical physicist, can't make it far, because it's so unlively that I don't get any intuition. Of course, math must be rigorous, because otherwise, it's no math, but a textbook should also convey the intuitive side at list a bit, and there I thought Arnold is one of the few modern textbook writers who provide both sides. My counter example is Dieudonne, whose analysis textbooks are a nightmare although for sure mathematically at top level.

 

[S.G. Janssens]

Uups?!?? If Arnold's book is sloppy, what do you think about the usual physics books then?

Sorry for being imprudent: I know you did not ask me the question, but I would like to comment that I often find physics (text)books pretty hard to read, because they are usually not written in the strict theorem-proof style that suits me. Nevertheless, I keep making an effort because I think that learning physics merely from the (applied) mathematics literature would make me miss out on lots of interesting work done by the physicists (and theoretically inclined engineers) themselves.

 

[vanhees71]

For me it's the opposite. I think the entire fun of math is gone in this boring theorem-proof style. That's a cultural thing. Math books weren't written always in this way. There are the famous books by Courant and Hilbert "Mathematische Methoden der Physik" or the series on analysis by Smirnov which are not written in this Bourbaki style. I guess this style is more suitable for original research papers than textbooks.

 

[slider142]

It only introduces differential geometry concepts when they are needed, right before Lagrangian mechanics is explored. So the latter half of the text is best explored after you have familiarized yourself with the language of differential geometry.
As for intuition, it may help a little, but intuition isn't really the domain of this particular text. Rather, it explores the details of what we must assume in order for the mathematical models of physical phenomena that we are used to to be viable, and the precise places where they are no longer viable, so that we can base our intuition on a solid background of non-contradiction, known curious behaviors, and a knowledge of the disconnect between rigorous mathematical models and physical reality.

 

[Mark Harder]

Do you think that these books-which are intended for mathematics students-would be helpful for me during a first course in Classical Mechanics?

While the history of physics is interesting, I don't think learning it will help you in your course. For one thing, 'modern' approaches to classical mechanics have gone way beyond Newton, and you need to learn these to understand how theoretical mechanics is done (assuming that's the goal of taking the course)

 

[Mark Harder]

Did you ask the course instructor for recommendations?