Intuition for Covariant derivative of a Tensor Field

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Discussion Overview

The discussion centers around gaining intuition for the covariant derivative of a tensor field, exploring the foundational concepts of tensors and their derivatives. Participants share resources and personal experiences related to understanding tensor analysis, with a focus on both theoretical and practical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses a desire to understand the covariant derivative of a tensor field, noting their grasp of vector fields but seeking deeper intuition about tensors.
  • Another participant recommends a NASA site for introductory tensor analysis, highlighting its coverage of scalars, vectors, and tensor types.
  • Some participants discuss the nature of the recommended site, with one questioning its commercial aspect due to its .com domain.
  • There is a suggestion to read a specific PDF related to tensor analysis, with participants sharing their positive impressions of the material.
  • One participant reflects on their initial struggles with tensors, describing the learning process as moving from manipulation of symbols to a better understanding of the underlying concepts.
  • A later reply suggests obtaining a Schaum's outline on Tensor Calculus as a supplementary resource to aid understanding.

Areas of Agreement / Disagreement

Participants generally agree on the value of the recommended resources for understanding tensors, but there is no consensus on the best approach to grasp the covariant derivative specifically, as individual experiences and interpretations vary.

Contextual Notes

Participants express varying levels of familiarity with tensors and the covariant derivative, indicating that foundational knowledge may be a limiting factor in understanding the topic fully. There are references to specific resources that may not cover all aspects of tensor analysis comprehensively.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to deepen their understanding of tensor calculus, particularly those struggling with the conceptual aspects of covariant derivatives and tensor fields.

maze
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Hi. I am attempting to gain some intuition for what the covariant derivative of a tensor field is.

I have a good intuition about the covariant derivative of vector fields (measuring how the vector changes as you move in a particular direction), and I understand how to extend the covariant derivative to tensors with the leibnitz product rule. I can calculate the tensor covariant derivative and prove things about it, but I still don't understand what it *is*.

Anyone?
 
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Basic Tensor Understanding

There is a site at NASA, that is a introduction to tensor analysis. It starts with scalars, vectors, dyads ...etc. It is an excellent paper to understand what is really going on with tensors, and its free. It also has co. and contra. variant tensors.

What a self promoting site. I cannot post the URL, because I have to make 15 posts or more. I am just trying to help someone. Thats what happens when a site starts to go commercial (Sci. Amer.). Contact me and I will e-mail the address.
 
well, you can't blame a site which ends with .com of being commercial.
 
I googled NASA tensor analysis, is this it:
gltrs.grc.nasa.gov/reports/2005/TP-2005-213115.pdf

?
 
I'm reading this pdf and so far it is rocking hard. nice.
 
I sent you the whole name. It is a little different, but you might have the same one, or a variant.
 
Thanks.
 
Your welcome. It is kind of like all the nuts and bolts you cannot get unless you get a really great teacher. It is real basic stuff, but I promise you will learn tensors and really understand what is going on at the root level.
 
I hope so. Right now working with tensors seems like a game you play by manipulating symbols according to random rules, although that is changing somewhat as I am reading the first pdf. After that, I'll get to the second pdf, and hopefully I'll be good after that.
 
  • #10
tensors

Forgot to tell you. After you read the pdf from nasa, get the schaums outline "Tensor Calculus", after those two things you will have no problem following any tensor book.

GOOD LUCK !
 

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