Tensor Analysis Books: Learn for Continuum Mechanics

[quasi426]

Does anyone know good books on tensor analysis, especially need to learn it to understand continuum mechanics. Thank you.

 

[robphy]

Here's a free one:
http://www.math.odu.edu/~jhh/counter2.html (see the bottom of the page)
and here are some notes
http://schubert.cse.bau.tu-bs.de/course-material/introduction-to-continuum-mechnics/tensor-calculus.pdf

 

[PerennialII]

... I'm still doing more than fine with Flugge's definite and compact -72 classic ... Tensor Analysis and Continuum Mechanics.

 

[leright]

Tensor Analysis by Michael J. Cloud. He's one of the EE profs at my uni. :D

 

[PerennialII]

Tensor Analysis by Michael J. Cloud. He's one of the EE profs at my uni. :D

Yeah, that's a good one. I've recently switched to the one by Talpaert which am liking quite a bit.

 

[Dr Transport]

I like the Continuum Mechanics Schaum's outline...

 

[Astronuc]

I am not familiar with the others, but I have a Dover book -

Mathematics Applied to Continuum Mechanics, by Lee A. Segel.

Chapter 1 - Vectors, Determinants, and Motivation for Tensors

Chapter 2 - Cartesian Tensors

The book is relatively inexpensive - I got it for $12.95 in the US last year.

I will have to check out the other books.

 

[rick1138]

I like the notes posted above. Excellent suggestion.

 

[rick1138]

By the way does anyone know of an in depth and complete refererence on the rules for index shuffling? The treatments I have found so far are somewhat ad hoc.

 

[robphy]

The classical (heavy-on-indices) tensor analysis texts include
Synge & Schild Tensor Calculus (now in Dover)

http://www.worldcatlibraries.org/wcpa/ow/dd096734b0aec209.html

Schouten Tensor Analysis for Physicists (now in Dover)

http://www.worldcatlibraries.org/wcpa/ow/f1eed175fa186e1a.html

Schouten Ricci Calculus (1954)
http://www.worldcatlibraries.org/wcpa/top3mset/683b0d0a4e09c701.html

The best way to learn is to do the calculations yourself (possibly after seeing someone else's derivation). You'll learn the necessary "index gymnastics". (Take advantage of symmetries!) However, it wasn't until I was introduced to the abstract index notation (see, e.g., Wald, General Relativity) that tensor analysis made more sense to me.

A good exercise is to take the tensorial form of Maxwell's Equations and use the decomposition by an observer (with a unit-timelike vector) to obtain the set of vectorial equations found in textbooks (and on t-shirts).

 

[rick1138]

Thanks for the links. Funny I saw someone just yesterday with the Mawell t-shirt - I was wondering why it didn't use the differential forms version - it would fit better on a t-shirt.

 

[quantumdude]

I like the Continuum Mechanics Schaum's outline...

And I like the Tensor Calculus Schaum's Outline.

quasi, those two together will run you about 30 bucks, which is a good deal.

 

[PhilG]

A Brief on Tensor Analysis by James Simmonds is very good.