What are some recommended books for graduate level classical mechanics studies?

[Robert1986]

I want a good book on classical mechanics - one that would be considered to be a graduate level text. The only Physics courses I have taken are the two standard intro physics courses taught at what seems to be every university, and a course in Computational Physics. My (relevant) math background is (feel free to ask me any other questions):

calc
ODE
PDE
various integral transformations

Thanks.

 

[jedishrfu]

goldstein's book on classical mechanics

 

[homeomorphic]

If that's your only background, I'm not sure you would want graduate level.

I like Vladimir Arnold's Mathematical Methods of Classical Mechanics, but for that, it might help to have done at least one proof-based math class.

 

[Robert1986]

If that's your only background, I'm not sure you would want graduate level.

I like Vladimir Arnold's Mathematical Methods of Classical Mechanics, but for that, it might help to have done at least one proof-based math class.

I'm sorry, my ignorance has caused me trouble. I'm currently a math grad student (or, well I will be one in a few days.) The reason I only listed the classes I listed is because I assumed those would be the only ones that would be relevant to classical mechanics. The reason for wanting a grad-level book is that I have to take three grad-level non-math classes.

For example, I've taken Analysis I&II, Algebra I&II, Combo. Analysis, Number Theory, etc

Would you change you recommendation with respect to grad-level books? Or would you suggest I read an easier book before the grad-level stuff?

 

[homeomorphic]

I'm sorry, my ignorance has caused me trouble. I'm currently a math grad student (or, well I will be one in a few days.) The reason I only listed the classes I listed is because I assumed those would be the only ones that would be relevant to classical mechanics. The reason for wanting a grad-level book is that I have to take three grad-level non-math classes.

For example, I've taken Analysis I&II, Algebra I&II, Combo. Analysis, Number Theory, etc

Would you change you recommendation with respect to grad-level books? Or would you suggest I read an easier book before the grad-level stuff?

No, in that case, Arnold's book is perfect.

These notes are also good:

http://math.ucr.edu/home/baez/classical/

 

[bcrowell]

I wouldn't leap straight from freshman physics to a graduate text on classical mechanics. When doing self-study, always start with a book that you're sure is too easy, and if you whip your way through that, move on to the next step.

Since the texts commonly used in freshman physics courses are crap, the first step I'd suggest is to read a good and rigorous freshman physics text. The classic is Kleppner and Kolenkow, An Introduction to Mechanics. Try working the hardest problems.

After that, the standard upper-division mechanics textbook is Goldstein, Classical Mechanics.

 

[Robert1986]

Alright, thanks guys! I think I'll start with Kleppner&Kolekow and Arnold.

 

[genericusrnme]

I personally like Landau and Lifgarbagez classical mechanics textbook more than goldstein's.
Kleppner is okay as an introduction book though.

 

[Mike706]

I personally like Landau and Lifgarbagez classical mechanics textbook more than goldstein's.
Kleppner is okay as an introduction book though.

I liked Landau and Lifgarbagez, as well. It was my first exposure, aside from high school physics and physics I. The first chapter gave me a little trouble because I had never seen calculus of variations before, but this lecture helped me a lot. The rest of the book was smooth sailing, and a really pleasurable read. There aren't many problems so - if you chose this book - make sure you solve all of the problems (and don't look at the included worked-solutions until afterwards!). You can always take the problems further than asked, as well, which will give additional insight. I find this tactic to be very helpful in books which do not give many practice problems. I love of the style of the L&L series books that I have used, so far.

That being said, I haven't worked through any other classical mechanics text in their entirety, so I can't comment on it being more or less appropriate. I am also currently under the impression that L&L does not cover all of the topics that Goldstein does (although you could certainly go back and study these after). It is certainly a smaller book, and very concise.

The best option is probably just to go to the library and find all the books you are considering. Read the prefaces and the first few pages of each; open the book to a few random spots and read a page or two. The most important thing in book choice is probably matching the author's writing style to the your personal "learning style", as this will allow you to get the most out of the book you chose.

 

[akai_ma]

a good math physics book might be a good idea too. Boas is the one I used as an undergrad. I liked it well enough. It does a decent job introducing the calculus of variations, and introduces tensor forms and a bit of differential geometry and has some good application problems.