Tensor Newbie trying to find Kolecki's rhythm

[jbowers9]

Re: Foundations of Tensor Analysis for Students of Physics and Engineering
with an Introduction to the Theory of Relativity
J.C. Kolecki
Glenn Research Center, Cleveland, Ohio

I'm currently reading the above monograph and I am attempting to teach myself TENSOR ANALYSIS. I have an undergraduates' degree in chemistry and a university level understanding of mathematics up to differential equations and some complex analysis. I've also taken introductory quantum chemistry so I have some facility - albeit incomplete - for mathematical formalism.
I can follow Mr. Kolecki's approach somewhat but get lost when he attempts to Q.E.D. some things. For clarity please see the attached file.

 

[Chris Hillman]

Hi, apparently you downloaded a document from NASA, which I see is available on microfilm at least one university library:

Kolecki, Joseph C, An introduction to tensors for students of physics and engineering , NASA Center for Aerospace Information, Cleveland, OH, 2002

Would you be willing to consider buying a standard printed texbook? Or borrowing one from your local research library? Can you give some context on your particular interest? What kinds of applications have you in mind?

Possible textbooks range widely, from a Schaum's outline text to Bishop and Goldberg or a modern book such as Darling. One textbook which I see is in at least one Chem research library is Ivan Sokolnikoff, Tensor analysis, theory and applications to geometry and mechanics of continua, Wiley, 1964.

 

[berkeman]

Here's a tutorial on tensors from the PF Tutorials forum in case it helps:

https://www.physicsforums.com/showthread.php?t=101414

 

[jbowers9]

Mr. Hillman,
Thank you for your prompt reply. My interest in tensors is of a purely
personal nature and is specifically geared towards my own intellectual development as I'm not associated w/any graduate level institutions but still have a deep interest in the subject. I do have an affiliation w/the NC State D.H. Hill library and could borrow any suggested texts if they have them available. The Kolecki paper is very good from an abstract point of view but I believe that in order to feel comfortable w/the material I need to solve problems. I would be willing to purchase a text as long as I can handle it. Otherwise it might end up as an obscure doorstop or paperweight. Again, thank you sir for your guidance.
John Bowers

 

[Thomas2054]

Also trying to find Kolecki's rhythm

John,

I am also reading this trying to better understand tensors for my own edification. It would be great to have someone of the same bent with whom to discuss this topic. I am an engineer and probably have about the same level of formal math training as you mentioned.

Let me know if you are interested.



Thomas

 

[uiulic]

MY point of view for an engineer:

A quantity is a tensor because WE SAY SO. The physicists have endowed some properties to the quantity.

 

[TyMoore]

Tensor Newbie

Hi, this is my first post. Really nice website--and I intend to be here many times!

I am also a "Tensor Newbie" and I have been trying to teach myself how to crunch them--

I am currently working my way through "Introduction to Vector and Tensor Analysis" by Robert C. Wrede copyright 1972 Dover Publications Inc. Very interesting stuff...

I also downloaded a copy of Kolecki's work--between that and my book and anything else I find along the way, I hope to be able to understand how to do the index gymnastics required...


I have an AA in Mathematics and Natural Science--I eventually hope to go back to school and get a mechanic engineering degree--but I love the math too. I am especially intruiged by General Relativity and Riemann Curvature Tensor and how it applies to gravity---

 

[jbowers9]

Tensor notation

I'd greatly appreciate a reference to a website where problems are worked out in tensor notation. I'm still shaky w/Levi-Civita notation and contraction of tensors - and why they are contracted in the first place. What happens to the dimensionality of the analysis after contraction?

 

[Chris Hillman]

Contraction is a kind of multidimensional analog of the trace.

You will need some kind of textbook if you want to learn this stuff, but you might want to also install a symbolic computation package so you can learn to make more involved computer-assisted computations. Maxima is free and Cal Tech offers a tensor analysis package. Maple, Matlab, and Mathematica are not free but offer more powerful packages.

 

[abcz1102]

I still feel confused about Einstein's notation. Who can give me some suggestion about this? Thank you !

 

[Reverie]

I still feel confused about Einstein's notation. Who can give me some suggestion about this? Thank you !

When one index is raised and one index is lowered, the summation symbol is omitted. There is nothing more to it. The main difficulty is accepting that such a convention is actually useful. It is useful because Einstein cleverly chose to make some indices raised and some indices lowered.

 

[jbowers9]

Indicial notation

But raised indices indicate contravariant. And lower indicate co-variant, correct? These are two independent coordinate frames of reference. What is the geometric interpretation of multiplying them?