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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1$\begingroup$ 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. $\endgroup$– wscCommented Apr 27, 2011 at 1:04
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$\begingroup$ 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. $\endgroup$– wscCommented Apr 27, 2011 at 1:06
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2$\begingroup$ If you are a math major, you maybe able to just start with Arnold's Mathematical methods of classical mechanics $\endgroup$– Willie WongCommented Apr 27, 2011 at 1:56
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$\begingroup$ 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. $\endgroup$– dmckee --- ex-moderator kittenCommented Apr 27, 2011 at 2:18
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1$\begingroup$ I like Landau and Lifshitz's mechanics, elegant and concise. But may not suitable for mathematician.... $\endgroup$– user26143Commented Aug 2, 2013 at 11:55
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8 Answers
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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 slowly. If that is too difficult then slooooowly. I'm pretty thick, to be honest, which is why I had no problem over the embarrassment 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 anywhere 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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4$\begingroup$ 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) $\endgroup$– wscCommented Apr 27, 2011 at 17:43
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3$\begingroup$ @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. $\endgroup$ Commented Apr 27, 2011 at 20:13
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1$\begingroup$ 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. $\endgroup$– XingdongCommented Apr 27, 2011 at 21:23
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$\begingroup$ @Xingdong, nowadays you can just read the reviews at amazon.com 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. $\endgroup$ Commented Apr 27, 2011 at 23:16
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$\begingroup$ I found the video classes given by Jacob Linder on classical mechanics really amazing. He follows the Goldstein book. He explain with few words, but in a insightful and simple way. I would start with that while doing the exercises in the goldstein book. yewtu.be/playlist?list=PLoRUNeJAicqbQPmKv3HNBIlcydy0CAI7k $\endgroup$– nadapezCommented Dec 6, 2021 at 1:08
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$\begingroup$ Ah! How could I have forgotten this one. $\endgroup$ Commented Apr 27, 2011 at 16:19
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3$\begingroup$ I never knew Spivak wrote on Class Mech!!! :-) $\endgroup$ Commented May 3, 2011 at 11:30
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2$\begingroup$ 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. $\endgroup$ Commented Aug 2, 2013 at 6:15
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$\begingroup$ @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. $\endgroup$ Commented Sep 27, 2015 at 4:41
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4$\begingroup$ alpha.math.uga.edu/~shifrin/Spivak_physics.pdf is the new (and working) link. $\endgroup$– MostafaCommented Jan 26, 2016 at 11:06
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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 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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1$\begingroup$ 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. $\endgroup$ Commented Apr 27, 2011 at 12:53
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3$\begingroup$ Did you just say Arnold lacks the soul of a physicist?
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1$\begingroup$ @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. $\endgroup$ Commented Apr 27, 2011 at 20:00
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$\begingroup$ @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. $\endgroup$ Commented Apr 27, 2011 at 23:02
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$\begingroup$ @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 formulain 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. $\endgroup$– Yai0PhahCommented Feb 2, 2014 at 18:36
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Besides Classical Mechanics What I have used in my studies is An Introduction to Mechanics.
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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:
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/index.htm
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:
http://www.youtube.com/watch?v=pyX8kQ-JzHI&p=189C0DCE90CB6D81
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You might be interested in Eugene Hecht's book: http://www.amazon.com/Physics-Calculus-Eugene-Hecht/dp/0534339859
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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$\begingroup$ Hecht is IMO only slightly above average for a recent, commercial text of its type -- which isn't saying much. $\endgroup$– user4552Commented Aug 12, 2011 at 2:30
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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