All Questions
Tagged with differentiation notation
14 questions with no upvoted or accepted answers
2
votes
0
answers
225
views
Thermodynamics Chain Rule And Independent Variables
I was reading my textbook and I came up across the entropy $S(T,V,N)$ where temperature $T$, volume $V$, and number of particles $N$ are the independent variables. According to the chain rule the ...
- 73
1
vote
0
answers
40
views
Mass Conservation in Kinetic Theory
In chapter 9 (The Boltzmann Equation) of Schwabl's 2006 text 'Statistical Mechanics', the author has the following statement of conservation of mass,
$$ \frac{\partial n}{\partial t} + \nabla \mathrm{...
1
vote
1
answer
164
views
Question regarding Energy Interaction of two particles
https://i.sstatic.net/LUsKX.jpg
To give a context as to what I'm asking here ,I am talking about the energy of a two particle system (section 4.9 Taylor's Classical Mechanics) .
My question is what ...
- 367
1
vote
1
answer
64
views
Convective derivative N-S
This is probably an easy answer, but I've not been able to find it yet -
Why in some formulations of the N-S equations (for example here https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html), is the $...
- 21
1
vote
1
answer
286
views
Covariant derivative with an upper index in terms of Christoffel symbols
I have encountered expression
$$\frac{1}{2}\left(2 \dot{g}_{\mu}{}^{\lambda ; \mu}-\dot{g}_{\mu}{}^{\mu ; \lambda}\right)$$
in a GR paper.
Here we assume to be working with the de Sitter metric $g$ ...
- 1,122
1
vote
0
answers
583
views
Partial derivative vs Total derivative
This is essentially a follow up to my question here since I seem to have some difficulties regarding the differences between partial and total derivatives.
Consider a Lagrangian density
$$\mathcal{...
- 1,674
0
votes
0
answers
159
views
What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$
What's the difference? $$\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$$
In John Dirk Walecka's book 'Introduction to General Relativity',...
- 51
0
votes
0
answers
110
views
Component notation and matrix notation for gradient of vector
I'm trying to understand vector and tensor notation, but I'm coming across some difficulties. Say I have vector $\vec{u}$ and I compute its gradient $\nabla \vec{u}$. Then I get a tensor $\frac{\...
0
votes
0
answers
109
views
Dirac spinor and derivative
I have question about four-derivative on spinors.
$$
\bar{\psi}\partial_\mu
$$
Does the derivative act on the spinor psi bar?
$$
(\bar{\psi}\partial_\mu)\psi
$$
$$
\bar{\psi}\partial_\mu\psi
$$
Is it ...
- 39
0
votes
0
answers
80
views
Why is cancellation of differnetial not allowed here?
This is about cancelation of differentials .I am learning basics of tesnor from "Mathematical Methods " by Boas. There I encountered this epression which author says are equal. $$ \frac{\...
- 128
0
votes
0
answers
138
views
Mathematical definition and notation of Fermat's Principle for least time
I was going through geometrical optics as it's a part of my undergrad course ,and I found about the Fermat's principle. The principle was understood but the mathematical equation given for it was not ...
- 345
0
votes
0
answers
359
views
Different subscripts for $\nabla$ operators while deriving force on system of many particles
Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system:
Total (external) force on ...
- 1,034
0
votes
0
answers
385
views
What is the meaning of symbols $\delta f$ and $\delta^2f$?
Professor was using these symbols to derive the continuity equation. He defined the infinitesimal mass as $\delta^2m=\rho \delta V$ and the mass that leaves some closed boundary $\partial V$ as $\...
-1
votes
1
answer
58
views
Expectation of partial time derivatives of $x$ in QM
In Ehrenfest theorem we know that
$$m\frac{d\left< x\right>}{dt}=\left< p\right>+m\left<\frac{\partial x}{\partial t}\right>.$$
So how can I exactly calculate a specific $\left<\...
- 11