What are some recommended books for understanding tensor analysis?

[srijithju]

Hi All ,
I am looking for a book on introduction to tensor analysis . I do not have much of a background in mathematics .. I have an undergraduate degree in engineering .

My aim is to understand General Relativity ... I would also like to understand Quantum Mechanics ... It feels odd that there are these great theories around and I do not even know enough to appreciate them .

When I was in class 12 ( in India we call it class 12 -the year before we join our undergraduate degree ... i donno what it is called elsewhere) , I picked up this book by J.Baggot "The meaning of quantum theory". After reading it I was completely enthralled by the world around us . During that time I read quite a few books on special relativity ( I must give note to a book by Resnick that I read and understood quite a bit ) and Quantum physics ... But at the time my knowledge of maths was very poor ( I knew only basic differential calculus and integral calculus - knew nothing of partial derivatives / multivariable calculus etc. ) , so i was unable to understand most of the content .
After that year .. I joined my undergraduate degree and in the 4 years there .. i hardly learned anything at all ( it is best not to talk about that period ).
Now I am past that period and would like to restore my interests in theoretical physics by self learning ( as other options to not seem to be feasible right now)

I know a little about multivariable calculus and diff equations , matrices , probability now .. but would need a refresher book for the same

For a person like me ( i am not too good at understanding math) ... what would be a good book / books that would teach me the basic maths required to understand general retivity , quantum mechanics , QFT .

I would also appreciate suggestions for introductory books on general relativity , quantum mechanics , QFT also .

Thanks in advance

 

[waht]

Being an engineering major, I've struggled learning general relativity from many books that physicists consider classics, such as Schutz, Walden, and MTH. Then I got hold of Hobson, and due its clarity breezed through it. It's undergrad level, and covers tensor calculus you need.

Same with QM, couldn't learn from Sakurai, Claude, Shankhar, Griffiths, and all the other goodies. Then tried Liboff, and resonated with the text. After learning from this book, all the other books don't seem so difficult after all.

I'm currently studying QFT from Srednicki, and glancing at Peskin once in a while. It's going slow, but making progress. Books that don't appeal is Zee, Ryder and Maggiore.

Hope that helps.

 

[jasonRF]

Most tensor analysis books I have found are incomprehensible. By far the best book on tensors that I am aware of is the book "a brief on tensor analysis' by simmonds. I worked through it myself after an undergraduate degree in engineering (after my first semester of grad school). If you know basic multivariable calculus and linear algebra you will be in good shape. The firsts two chapters are quite straightforward, while the last two will take more work.

You may be able to find other books online that are okay - but I am assuming you have already googled.

good luck.

Jason

 

[jasonRF]

Being an engineering major, I've struggled learning general relativity from many books that physicists consider classics, such as Schutz, Walden, and MTH. Then I got hold of Hobson, and due its clarity breezed through it. It's undergrad level, and covers tensor calculus you need.

Same with QM, couldn't learn from Sakurai, Claude, Shankhar, Griffiths, and all the other goodies. Then tried Liboff, and resonated with the text. After learning from this book, all the other books don't seem so difficult after all.

I'm currently studying QFT from Srednicki, and glancing at Peskin once in a while. It's going slow, but making progress. Books that don't appeal is Zee, Ryder and Maggiore.

Hope that helps.

By the way, Liboff was an electrical engineering prof., so he was used to teaching engineers. I learned from his book too - I was a student in his dept., but my prof used no textbook to teach the class. I learned more from Liboff than my prof!

 

[srijithju]

Thanks a lot .. I had a peek at "A brief on tensor analysis" by Simmonds on google books ... it seems like the book I'm looking for ... looks like it is concise .. and by the contents .. the 1st chapter seems to be vectors , and the last chapter seems to be about curl divergence , gradient etc .. I have already some background of these operators for vectors .. so seems like i should be able to understand it.

But this book doesn't seem to have an economy edition for countries like India .. so it might just be a a bit too expensive ...

But I checked Liboff .. and for this book there is indeed a economy edition available .. so I should be able to purchase it ...

Any other suggestions ..

 

[Daverz]

GR and QM books have been covered very thoroughly in the forum, so please take a look at some of the older threads.

For GR, I'd start with Hartle's Gravity, which emphasizes Physics.

Form math review, Shankar's Basic training in mathematics: a fitness program for science students looks like it may fit the bill. Also the Schaum's Outline of Advanced Mathematics for Engineers and Scientists.

 

[diogenesNY]

srijithju--

would this help? --:

http://www.betterworldbooks.com/A-Brief-on-Tensor-Analysis-Undergraduate-Texts-in-Mathematics-id-038794088X.aspx

diogenesNY

 

[RedX]

I suggest "Tensor analysis and continuum mechanics" by Wilhelm Flügge because it is very easy, and since you're an engineer, it will benefit you by teaching you continuum mechanics. It's a very thin and (relatively) old book so hopefully it's not expensive.

 

[Pinu7]

https://www.amazon.com/dp/0486661105/?tag=pfamazon01-20 by Aris has a soft introduction to tensor analysis as well as one of the best introduction to fluid mechanics I have ever seen.

https://www.amazon.com/dp/0486640396/?tag=pfamazon01-20- Bishop, Goldberg an incredible book all around.

Also, an online book:
http://uk.arxiv.org/abs/math/0403252/

 

[n!kofeyn]

https://www.amazon.com/dp/0486640396/?tag=pfamazon01-20- Bishop, Goldberg an incredible book all around.

I came here to post this book as well.

If general relativity is your goal, then I would suggest https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20 by Sean Carroll. It's probably the newest of the top general relativity books, and it builds up the necessary prerequisites.

 

[jonjacson]

I am reading the book from borisenko and taraponov, and for me it is excellent. Recommended, you can se it at amazon, a lot of examples, clear ideas...