A Student's Guide to Vectors and Tensors

[Student100]

Has anyone actually gone through this book? I was looking for something that explained tensors a bit clearer and came to this book. It has pretty good reviews, but I was wondering if anyone here has anything to add or suggestions.

https://www.amazon.com/dp/0521171903/?tag=pfamazon01-20

 

[WannabeNewton]

Just out of curiosity, how rigorous an introduction to tensor analysis do you want/need? Do you need it at the level of a mathematics student or at that of physics student etc.? Any particular subject you're studying or attempting to study that requires you to learn tensor analysis beforehand?

 

[Student100]

Physics level WBN, doing GR next quarter. I've read Boas chapter on tensors, and aside from touching on them in E&M2, I've not really dealt with them. Maybe I'm overthinking how much I need to know about tensors at this point, but I feel like I have quite a few holes in my understanding. :p

Course description.
Topics covered in the first quarter include special relativity, differential geometry, the equivalence principle, the Einstein field equations, and experimental and observational tests of gravitation theories.

 

[WannabeNewton]

Physics level WBN, doing GR next quarter.

Haha now we're talking

I've read Boas chapter on tensors, and aside from touching on them in E&M2, I've not really dealt with them. Maybe I'm overthinking how much I need to know about tensors at this point, but I feel like I have quite a few holes in my understanding. :p

It's quite possible that you are overthinking it; regardless, practice makes perfect so you can't lose by doing more

However looking through the text you linked I would not recommend it for the purposes of GR. There are a couple of reasons for this:

For one that book (as well as Boas) are very low brow when it comes to tensors.

Second, and more importantly, most standard GR texts do a superb job of introducing tensors at the appropriate level and with the appropriate style for GR so you would be spending extra money for less gain by getting a separate book just for tensors.

Do you happen to know what GR text you will be using next semester?

 

[Student100]

Do you happen to know what GR text you will be using next semester?

Looks like Bernard Shutzs a first course into general relativity , and the professors notes.

 

[WannabeNewton]

Looks like Bernard Shutz, and the professors notes.

Schutz has a brilliant, modern coordinate-free exposition of tensors at a level appropriate for physics undergrads (it was my first textbook on GR and I loved it to death); you won't need to waste your money on the book you referenced in the OP. If you want more rigorous treatments of tensors in the context of GR then I'll be happy to give references.

 

[Student100]

Schutz has a brilliant, modern coordinate-free exposition of tensors at a level appropriate for physics undergrads (it was my first textbook on GR and I loved it to death); you won't need to waste your money on the book you referenced in the OP. If you want more rigorous treatments of tensors in the context of GR then I'll be happy to give references.

Appreciate it WBN! I'll keep you in mind as I go through the course. ;)

 

[WannabeNewton]

You probably already know this but GR is one of those subjects where you need multiple textbooks in order to get a strong grasp of both the physical concepts and the mathematics underlying GR. Both of course can only be grasped strongly by doing problems.

From personal experience I found that Schutz did the math part quite well at the undergrad level but not so much the physical concepts part, at least not in terms of problems. I'm sure your professor has his own problem sets to give out that don't come directly from Schutz but if you want to splurge on an extra textbook for extra practice with problems and whatnot then I would really recommend another gem of GR pedagogy: https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20

I've done a lot of the problems in Hartle in the past and I can say that the problems in Hartle are infinitely better than the ones in Schutz for grasping the physical concepts underlying GR. In my opinion it is the physical concepts of GR that are harder to really get a mastery of; the mathematics is easy. There are also a lot of little things here and there that Hartle expounds upon, things that Schutz either never even mentions or explains incorrectly (e.g. the operational construction of an experimental laboratory using Lorentz frames, the operational difference between a coordinate system and a Lorentz frame, all the little box discussions reminiscent of MTW).

Check it out if you can and have fun!

 

[Daverz]

Boas is not "low brow"; the coverage is appropriate for the audience.

I'd also recommend the other book by Schutz: Geometrical Methods of Mathematical Physics

https://www.amazon.com/dp/0521298873/?tag=pfamazon01-20