Oh, yes, that is a typo. It is meant to be a ##\partial## not a ##\phi##. My decision to call the sum index ##i## was just because the derivative was taken with respect to ##\phi^{i,j}## but this might be bad practice. I'm not familiar with the conventions people use when using tensors because...
Homework Statement
Hi all, I'm trying to learn how to manipulate tensors and in particular to differentiate expressions. I was looking at a Lagrangian density and trying to apply the Euler-Lagrange equations to it.
Homework Equations
Lagrangian density:
\mathcal{L} = -\frac{1}{2}...
Ahhhh that makes perfect sense! So would it be accurate to say that (for conservative fields):
- whenever you aren't integrating on a path, you have to use an exact derivative as you don't know the relationship between x,y,z?
- when you choose a path, then you know how x,y,z vary wrt each...
I meant that x\ dy + y\ dx = d(xy) and therefore I don't understand why you have need to use the exact RHS to get the correct answer out? And likewise for the other differentials.
Ah right, so it's all line integrals then. Sounds fun. :P
Thanks, I hope so! It will be tough, no doubt, but I...
Interesting, both failures are due to the same thing really aren't they? Though I see immediately that the right answer comes out when the product rule is used, I am confused as to why it doesn't work without this - as the two are equal, are they not? Nevertheless, thank you for that insight as...
Hey guys and gals, this isn't actually an assignment of any sort, so I didn't want to put it in the homework section. This is also my first post, though I have been lurking for quite a while, reading the copious amounts of information available here. :p
Anyhow, could somebody please elaborate...