Tensor Analysis Books: Learn for Continuum Mechanics

In summary: Worth the cost if you're serious about learning tensor analysis.By the way does anyone know of an in depth and complete refererence on the rules for index shuffling?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.
  • #1
quasi426
208
0
Does anyone know good books on tensor analysis, especially need to learn it to understand continuum mechanics. Thank you.
 
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  • #2
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
 
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  • #3
... I'm still doing more than fine with Flugge's definite and compact -72 classic ... Tensor Analysis and Continuum Mechanics.
 
  • #4
Tensor Analysis by Michael J. Cloud. He's one of the EE profs at my uni. :D
 
  • #5
leright said:
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.
 
  • #7
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.
 
  • #8
I like the notes posted above. Excellent suggestion.
 
  • #9
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.
 
  • #10
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).
 
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  • #11
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.
 
  • #12
Dr Transport said:
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.
 
  • #13

FAQ: Tensor Analysis Books: Learn for Continuum Mechanics

1. What is tensor analysis?

Tensor analysis is a branch of mathematics that deals with the study of geometric objects called tensors. Tensors are mathematical objects that can be represented by multidimensional arrays and are used to describe physical phenomena in fields such as continuum mechanics.

2. Why is tensor analysis important in continuum mechanics?

Tensor analysis is important in continuum mechanics because it provides a mathematical framework for understanding the behavior of continuous materials such as fluids and solids. Tensors are used to describe the properties of these materials, such as stress, strain, and deformation, and are essential for solving equations and making predictions in continuum mechanics.

3. What are some common applications of tensor analysis in engineering?

Tensor analysis has many applications in engineering, including fluid mechanics, solid mechanics, structural analysis, and electromechanics. For example, in fluid mechanics, tensors are used to describe the properties of fluids and the flow of fluids through pipes and channels. In solid mechanics, tensors are used to describe the stress and strain in materials under different loads and conditions.

4. Are there any prerequisites for learning tensor analysis for continuum mechanics?

Yes, a basic understanding of vector calculus and linear algebra is necessary for learning tensor analysis for continuum mechanics. It is also helpful to have knowledge of differential equations and mechanics, but these topics can be learned concurrently with tensor analysis.

5. What are some recommended books for learning tensor analysis for continuum mechanics?

Some popular books for learning tensor analysis for continuum mechanics include "Tensor Analysis for Physicists" by Wolfgang Rindler, "Tensor Analysis: Theory and Applications" by I. S. Sokolnikoff, and "Continuum Mechanics and Tensor Analysis" by R. C. Mowrey. It is also helpful to consult textbooks on continuum mechanics that include chapters on tensor analysis, such as "Introduction to Continuum Mechanics" by David J. Raymond.

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