What is the best mathematics book for physicists?

[AhmedHesham]

what is the best mathematics book for physicists ?or in what way should i study math if i need it for physics? . thanks!

 

[jedishrfu]

One popular one is the Arfken and Weber book:

https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20

and another Boas:
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

 

[AhmedHesham]

thank you very much . is it better to read both of them or one is enough ?

 

[jedishrfu]

Hard to say, sometimes you need to look in several books until you find what you're looking for.

I think Arfken and Weber is good for practicing physicists whereas Boas is a good undergrad book. I've heard a lot of good reviews about the Boas book. I have a copy of Arfken and Weber and like the style of presentation.

There's also the Nearing book which is available online which you could start with:

http://www.physics.miami.edu/~nearing/mathmethods/

 

[Bong_Nebula]

Absolutely avoid Cahill. It's nearly worthless unless you already know the concepts and just need a refresher.

 

[AhmedHesham]

ok . thank you so much

 

[AhmedHesham]

ok
Bong_Nebula

 

[carollbert]

Sean Carroll's lecture notes on general relativity contain a superb introduction to the mathematics of GR (differential geometry on Riemann manifolds). These also also published in modified form in his book, Spacetime and Geometry.

Spivak's Calculus on Manifolds is a gem. Bishop's Tensor Analysis on Manifolds is a great introduction to the subject, and published by Dover, is very cheap (less than $10 on amazon).

Georgi's Lie Algebras in Particle Physics is enjoyable and fast-paced, but probably skips around too much to be used as an adequate first exposure.

Shutz's Geomertical Methods of mathematical physics and a first course in general relativity.

Despite it's incredibly pompous title, Penrose's The road to reality: A completer guide to the laws of the Universe provides an enjoyable high-level view of a vast expanse of mathematical physics.

As mentioned by Cedric, I am a huge fan of Sussman and Wisdom's Structure and Interpretation of Classical Mechanics and the associated Functional Differential Geometry memo. The citations in those publications will also point to towards a lot of good material and there's more goodies if you dig around in the source code.

 

[jasonRF]

AhmedHesham,

How much math do you already know? How much physics?

jason

 

[AhmedHesham]

AhmedHesham,

How much math do you already know? How much physics?

jason

I know some algebra , some geometry and some calculus only . in physics I know elementary things about classical mechanics and electromagnitism

 

[AhmedHesham]

Sean Carroll's lecture notes on general relativity contain a superb introduction to the mathematics of GR (differential geometry on Riemann manifolds). These also also published in modified form in his book, Spacetime and Geometry.

Spivak's Calculus on Manifolds is a gem. Bishop's Tensor Analysis on Manifolds is a great introduction to the subject, and published by Dover, is very cheap (less than $10 on amazon).

Georgi's Lie Algebras in Particle Physics is enjoyable and fast-paced, but probably skips around too much to be used as an adequate first exposure.

Shutz's Geomertical Methods of mathematical physics and a first course in general relativity.

Despite it's incredibly pompous title, Penrose's The road to reality: A completer guide to the laws of the Universe provides an enjoyable high-level view of a vast expanse of mathematical physics.

As mentioned by Cedric, I am a huge fan of Sussman and Wisdom's Structure and Interpretation of Classical Mechanics and the associated Functional Differential Geometry memo. The citations in those publications will also point to towards a lot of good material and there's more goodies if you dig around in the source code.

Thanks
carollbert

 

[jasonRF]

I know some algebra , some geometry and some calculus only . in physics I know elementary things about classical mechanics and electromagnitism

In that case, you probably should learn linear algebra, multivariable calculus and basic differential equations before reading even the most basic of the books listed by others here (Nearing: http://www.physics.miami.edu/~nearing/mathmethods/; and Boas).

Books on Lie algebras, general relativity, differential geometry, etc. are way beyond your level at this point. (They are probably beyond my level, too!)

jason

 

[jasonRF]

There are many books on calculus that fit the bill for your next step (multivariable calculus, elementary vector calculus). I learned from Thomas and Finney 7th edition (https://www.amazon.com/dp/0201163209/?tag=pfamazon01-20) but many folks here think that the 3rd edition is superior to all the rest (https://www.amazon.com/dp/B00GMPZBGA/?tag=pfamazon01-20)

For linear algebra, a good free book is by Hefferon, free at:
http://joshua.smcvt.edu/linearalgebra/
but you can also buy a paperpack if you like hardcopy better: https://www.amazon.com/dp/0989897567/?tag=pfamazon01-20
Many other books exist - search physicsforums for linear algebra books and you will find many results

There are many differential equations books. I do not know what is best.

jason

 

[AhmedHesham]

thanks very much