what i did was (p+dp)^(q+dq) -p^q. i evaluated that and got + p^dq +dp^q +dp^dq
what do we do with that? Wher do the other parts come in?
Again I'm sorry for my stupidity.
Oh no. it's simply the wedge product thing. anyway could you write out an example because i don' think I got that(unless i arranged the terms wrong which i rpobably did without noticing).
I know this is stupid, but please do this for me. I know its weird and stupid...
i'm awful with...
I was talking about the exterior derivative of a wedge product.
It's suppose to be something like, p^dq +-1^p (q^dp) or something along those lines. how do we get that?>
i know its silly but i really don't know how its proven.
So I did understand it. One last thing, I'm not sure if I understand the modified leibniz rule very well. could someone prove it rigorously?
I'm talking about the liebniz rule between wedge products. I don't quite know how to prove it...:(
It is probably beyond me at this moment as i don't know about those. I don't really mind. at least you were polite about it. so intuitively speaking it's just like the fundmanetal theorem?
I don't think I'll be ready for awhile, but this boredom is really getting to me. I literally have...
I was wondering as to how to prove stokes theorem in its general and smexy form.Also what is the intuition behind it(more important) aside from the fact that its a more general form of the other theorems from vector calculus?
how does one derive the general formula for the covariant derivative of a tensor field? To be more precise I took out sean carolls book at the library but did not understand equation 3.17 on page 97. Could someone derive it or prove it, or at the very least give me a better hint?
Yes but I really think that if i am to understand this topic the right way, i need to find myself a math not book. Physics books are not really enough beyond the tensor analysis section, and I realize that things like connection exist for a reason. So i'll take the masochistic root. do you know...
Yah I know what it is now but computations with it seems nigh impossible. Ok this question is stupid, but can't we just use the chain rule to calculate the directional derivative of a tensor field in an arbitrary direction(byt that I mean can the directional derivative be written as a linear...
what is a good book in differential geometry. I currently know calculus, a bit about differential equations, a bit of linear algebra and a bit about tensors. I also know some variational calculus.
Of course what I know won't really help. I've skimmed through some physics sources and...
That should be very interesting. The few moments I've had with mathematicians were the highlights of 2006! For now it won't be possible, becuase the university of toronto's math department contact page is inaccesbile.
http://www.math.utoronto.ca/
check for yourself.
i have however contacted...
I've never found a resource on complex analysis, I am VERY interested in ANY introduction to rigorous mathematics.chern chem and lam? what's the book like? does it start with gaussian geometry or full blown generality?
I'd actually prefer to study mathematics outside of physics but i can't...
Ah ok I understand. Yes it's actually very simple now. It's just that when I was introduced to it, it was this weird alien symbol who's significance i could not grasp.
I know I'm stupid. I have no illusions about that.
Luckily I understand it now.
As for gauss' law for inverse square...
green's theorem says that the circulation is around an interval is equal to the sum of iinfintessimal circulations within the area. Say that you have a square, you can find the cxirculation around it through very simple methods. then put another square beside it and calculate it's circulation...
I know some university level classical dynamics, special relativitivistic kinematics and dynamics. I also know a bit of electromagnetism.
That stuff was all pretty easy, though the complete lack of rigour that physicists use when explaining gauss's law is insulting.
I know enough physics...
Ok I get 3.12 but am still having trouble withthe material at the beginning of page 70. it would be nice if someone pmed me, but posting here would be OK. I'm really sorry btw. These are the few topics I've been having trouble with. i rarely ask things online.
Please try to epxlian it to me...
the sixteen component thing seems so obvious now. so what your saying is that the most general possible 0,2 tensor has sixteen components? That makes sense.
however i don't understand the significance of the kronecker delta thing. that well at least. Oh wait.
I'm still having a hard time...
i'm not sure if i understand 3.12 properly. I'm not too well versed in the kronecker delta. I will give it a shot though.
I think it means that the output can only equal the correspong components multiplied together IF the basis one form applied to the basis vectors equal some identity map...
Ah that was just a simple misunderstanding. however there is another section i have a hard time with. It's on page 70. It's the part where they talk about the absis of the gradient one form. i don't quite understand what's being done. could you guide me through it step by step?
I'm finding...
How can we prove that the tensor product between two tensors of lower rank forms the basis for ANY tensor of higher order? also WHY is it it true?
ANY TENSOR of higher order.