Shortest Paths

[□h=-16πT]

Do you think I can handle your discussion?

 

Yeah, I would have thought so. Just keep going with your linear algebra and continue with tour research into tensor algebra (or even get a book out from a library on it). It's taking me so long because I was busy over the weekend and the exam period is approaching quickly.

[Johnny5]

Yeah, I would have thought so. Just keep going with your linear algebra and continue with tour research into tensor algebra (or even get a book out from a library on it). It's taking me so long because I was busy over the weekend and the exam period is approaching quickly.

 

That's what I'll do then.

 

Regards

[□h=-16πT]

That's what I'll do then.

 

How's that going?

[Johnny5]

How's that going?

 

It's going ok, I run through things at home at night.

 

I have been looking for the book I first learned it from, all over the house in fact, and can't find it. I could finish that book in 2 days.

 

Right now, all I have is Schaum's outline, but it will have to do if I can't find my old text.

 

Well no that's not true, I have a few books, but I know which one would go the quickest.

 

In all honesty, I have been learning quite a few new things about astronomy, which are fascinating. But this weekend I will have some time, so ask me the same question monday.

 

Regards

[□h=-16πT]

Ok then. If you want to get into some advanced stuff on geometry get "Geometrical methods of mathematical physics"-B. Schutz. I've recommended it to you before, but it really is excellent and I believe it's very popular with theoretical physicists. It starts at the basics: tensor algebra; discussion of manifolds; fibre bundels etc. It then advances through things such as Lie derivatives and Lie groups; killing vectors; differential forms and their calculus; applications to theoretical physics, all sorts of stuff (I'm not that far into it at the moment). The other book by Schutz that I've recommended omits one or two topics from the above book that aren't of great relevance to a first course in GR.

 

I will do that Riemann tensor thing this weekend by the way.

[□h=-16πT]

Ok, so I didn't get it written, sorry. How's your revision doing though?

[Johnny5]

Ok, so I didn't get it written, sorry. How's your revision doing though?

 

Revision?

 

You mean review.

 

It's going. I have been gathering some books on other topics, and reading.

 

There are some other things I am working on first.

 

But obviously I have to regain the linear algebra information, so that has to happen. But I want it done right.

 

I have gone through the Gauss elimination method many times. That's not a problem, and honestly I never forgot how to do it.

 

And I remember how to multiply matrices together too.

 

The thing I wanted to work on next, was knowing what the answers mean, after you get the coefficient matrix into row echelon form(i think thats what its called zeros everywhere ones down the main diagonal).

 

Like, suppose you are dealing with equations for planes.

 

You are in three dimensional space.

 

And you get something inconsistent, like 0=2, after you did all that work.

 

What exactly does that mean? That the planes are parallel?

 

And also, if underdetermined... I forget how you write the answer.

 

Something like (3,2,4) + r(0,0,1)

 

you get these arbitrary scalars in your answer.

 

I forget that.

 

I was hoping to find my original textbook, but I still haven't located it.

 

 

Oh and I was reading up on eigenvectors and eigenvalues of a matrix just yesterday.

 

It will come back, but i've been reading up on some things in real analysis lately. Convergence of series, that kind of thing.

[□h=-16πT]

Right then, Johnny, you want to get this going again? That is if no admins object.

[Johnny5]

Right then, Johnny, you want to get this going again? That is if no admins object.

 

 

Yes, that sounds good, we can pick up from wherever.

[□h=-16πT]

Seeing as this thread has more or less dried up, have a read of this .pdf and we can make any problems you have with it topics of discussion. The .pdf has subsequently been published as a book on GR, so it will be better at explaining topics better than I will.

 

Carrol lecture notes on GR

 

I've read the bits of interest to me and I must say he's a good writer.

[Johnny5]

The .pdf has subsequently been published as a book on GR' date=' so it will be better at explaining topics better than I will.

 

Carrol lecture notes on GR

 

 

Well then we can discuss the .pdf, starting with the beginning, and moving fowards, I just read the opening few paragraphs, and they start at SR, in order to introduce tensors.

 

So maybe we should start there. Since I don't already know tensor calculus, you can teach me that. I know we've discussed tensors before, and it will be interesting to see how much i remember. Additionally, since the last time we talked, i discovered that it was Hamilton who introduced the term 'tensor' in his lectures on quaternions, in the 1800's.

 

So how about start off with a bit of tensor analysis?

[□h=-16πT]

Ok, well I'll put something together about the basics and then I think it would be fairly interesting to move onto manifolds so that we can get bits about differential forms and the lie and covariant derivatives etc in.