# Intuition for Covariant derivative of a Tensor Field

#### maze

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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#### russelljbarry15

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.

#### MathematicalPhysicist

Gold Member
well, you can't blame a site which ends with .com of being commercial.

#### maze

I googled nasa tensor analysis, is this it:
gltrs.grc.nasa.gov/reports/2005/TP-2005-213115.pdf

?

#### maze

I'm reading this pdf and so far it is rocking hard. nice.

#### russelljbarry15

I sent you the whole name. It is a little different, but you might have the same one, or a variant.

Thanks.

#### russelljbarry15

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.

#### maze

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.

#### russelljbarry15

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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