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I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through Goldstein's Classical Mechanics. What books would be good for a beginner?

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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

Not sure why this was closed... it seems like there have been a lot of these in the past that have survived. Anyway, K&K is a good book, but there's supposed to be a new edition coming out, so I'd wait for that. Hand & Finch is one of my favorites with an awesome selection of practice problems. And regardless, Goldstein is a totally fine starting point -- I'm not sure why people think it's necessary to get some "beginner" book to prepare for it but if you're willing to read carefully and do problems it's really not so hard. – wsc Apr 27 '11 at 1:04
Also -- for a math major, Jose & Saletan is a neat book that tends to frustrate physics undergraduates (and grad students!) but might be up your alley if you have a differential geometry bent. – wsc Apr 27 '11 at 1:06
If you are a math major, you maybe able to just start with Arnold's Mathematical methods of classical mechanics – Willie Wong Apr 27 '11 at 1:56
As to why it was closed, I followed mbq's move on the last one of these. Moderators are discussing it now, and it is likely that we will suggest a change and re-open it. – dmckee Apr 27 '11 at 2:18
I like Landau and Lifshitz's mechanics, elegant and concise. But may not suitable for mathematician.... – user26143 Aug 2 '13 at 11:55

Assuming that you have studied introductory mechanics at the level of freshman physics, The best book on mechanics after that to tackle is Classical Mechanics by John R. Taylor. It is very clear and insightful. The author is a very good writer, he has written also the best introductory book on error analysis.

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Goldstein's Classical Mechanics is a masterpiece. That's why it's still held in such high regard as one of the best mechanics books available 60 years later after after 3 revisions.

I would suggest that you should stick with this book and work through it sloooooooooooooooooooooooooooooooowly. If that is too difficult then sloooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooowly.

I'm pretty thick, to be honest, which is why I had no problem over the embarrassement of taking a week trying to understand a page of the first chapter sometimes. Others would take a month, and others I still don't understand fully.

I don't think any book comes anywere close to explaining mechanics concisely and accurately in the first chapter, where others take 300 pages and yet still gloss over the details.

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Landau & Lifshitz of course treat classical mechanics with perfect accuracy and very very concisely. There's no shame in spending a long time with a good book and I think it's silly to believe you have to spend a long time with a book that isn't as good to get "ready" for the real stuff (and weightlifting analogies will never convince me! ;p) – wsc Apr 27 '11 at 17:43
@wsc, i think L&L is good only for people that have a good understanding of mechanics already. The book starts with the Lagrangian as a postulate, missing out Newton's laws from the start. – John McVirgo Apr 27 '11 at 20:13
Generally, how do you select or say filter the perfect books ? Because when I need to learn one topic, I always search the term at Amazon, and it shows tons of books, but I don't know how to find out some best books. Is there some tips or criteria for that ? Like try to use the book written by famous masters in the certain area, say Nobel prize winner. Like Abel said that, read the masters not the pupils, especially today we have too many things to learn about within limited time and energy. But it is not the case that we can find a book in a certain topic written by famous masters in it. – Xingdong Apr 27 '11 at 21:23
@Xingdong, nowadays you can just read the reviews at on some standard mechanics text book and see what other books they recommend. for example, some of the comments for Goldstein recommend Classical Mechanics [Hardcover] John R. Taylor. – John McVirgo Apr 27 '11 at 23:16

Start here:

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Ah! How could I have forgotten this one. – Willie Wong Apr 27 '11 at 16:19
I never knew Spivak wrote on Class Mech!!! :-) – Debangshu May 3 '11 at 11:30
Yes. In fact he ended up publishing a textbook called Physics for Mathematicians, Mechanics I which, I should add, I really like. Not quite as amazing and concise as Calculus on Manifolds, but that's understandable given that physics is messy. – joshphysics Aug 2 '13 at 6:15
@joshphysics I agree that this is a very impressive book,but it's hardly for the average undergraduate in mathematics.They'd need at least a first year graduate course in differential geometry to read it effectively. – The Mathemagician Sep 27 '15 at 4:41
1 is the new (and working) link. – Mostafa Jan 26 at 11:06

Goldstein is good. However, since you are anyways a math major, you can easily start off with Jose and Saletan or Arnold's Mathematical Methods of Classical Mechanics. There are other books like Hand & Finch and definitely the classics by Landau.

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I don't like Arnold's book at all because it lacks the soul of a physicist and comes across as cold. He defines the degree of a system in terms of a differential equation, for example, whereas Lagrange defined it as the number of variables needed to define the state of a mechanical system. – John McVirgo Apr 27 '11 at 12:53
Did you just say Arnold lacks the soul of a physicist? :-) – Willie Wong Apr 27 '11 at 16:19
@Willie, I said his book lacks the soul of a physicist, but it's a book about the mathematics of mechanics after all. A great book with the soul of a physicist is The Variational Principles of Mechanics by Cornelius Lanczos. Too advanced for the OP, though. – John McVirgo Apr 27 '11 at 20:00
@John JFYI, I didn't receive a notification for the comment you just wrote. I suspect it is because you put a comma immediately after my name and the @-notification system choked. – Willie Wong Apr 27 '11 at 23:02
@WillieWong I don't know why V.I.Arnold suggested Landau & Lifschitz. Apparently, Arnold paid much attention on geometric meaning. In his words, In accordance with this principle there are many figures in the book, but not a single complicated formula in his ODE textbook. However, as far as I read Landau, so much attention is paid on seemingly blind calculations. That's what Arnold criticized a lot in many occasions. – Frank Science Feb 2 '14 at 18:36

Besides Classical Mechanics What I have used in my studies is An Introduction to Mechanics.

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You might be interested in Eugene Hecht's book:

What I like about it is that both fundamental principles (notably Noether's principle) and basic but important techniques (like dealing with significant digits) are consistently mentioned and enforced throughout the book. It also contains a lot of examples and exercices of varying levels of difficulty.

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Hecht is IMO only slightly above average for a recent, commercial text of its type -- which isn't saying much. – Ben Crowell Aug 12 '11 at 2:30

I think Goldstein is a great book which should be supplemented by the internet, rather than a mass of books to clarify every detail.

There's the MIT OpenCourseWare program for classical mechanics:

Here you'll find the videos by prof Lewin, lectures notes, exam questions, study groups etc.

There's also the 10 classical mechanics videos by Prof Susskind of Stanford, but on a level around that of Goldstein:

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Since I'm not a math major and have little direct experience with math people learning physics, my answer here is pure speculation. I'll offer it anyway.

You don't want something like Arnold's mathematical book on mechanics. That would be new material, but essentially familiar to you and inside your comfort zone. If you're interested in learning physics for its own sake, what you want to focus on isn't the mathematical structure of the theory, but the physical intuition, since that's where you pick up something new and exciting.

In that vein, I recommend

Thinking Physics by Lewis Carroll Epstein

The Feynman Lectures on Physics

The Mathematical Mechanic by Mark Levi

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