Linked Questions

1
vote
0answers
615 views

How is $\delta s$ different than $ds$? [duplicate]

Specifically I'm reading Dirac's General Relativity and he says essentially: $$ \delta Q = \frac{\partial Q}{\partial x^\mu} \delta x^\mu $$ But what's the difference between this and: $$ dQ = \...
0
votes
0answers
45 views

$\delta Q = dU + \delta W$. Why is it $dU$ while others are partial differentials? [duplicate]

It is the first law of thermodynamics for a very small change in the state of the system. It is in Heat thermodynamics and statistical physics by Brij Lal, Dr. N. Subrahmanyam, and P.S. Hemne.
43
votes
3answers
16k views

What is the difference between implicit, explicit, and total time dependence, i.e. $\frac{\partial \rho}{\partial t}$ and $\frac{d \rho} {dt}$?

What is the difference between implicit, explicit, and total time dependence, i.e. $\frac{\partial \rho}{\partial t}$ and $\frac{d \rho} {dt}$? I know one is a partial derivative and the other is a ...
35
votes
2answers
36k views

Difference between $\Delta$, $d$ and $\delta$

I have read the thread regarding 'the difference between the operators $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In Mathematics, $\...
6
votes
5answers
3k views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
1
vote
1answer
743 views

From master equation to Fokker-Planck equation

For the continuous master equation in real space and time, we have for the distribution $f(x,t)$: $$\frac{\partial f(x,t)}{\partial t}=\int_{-\infty}^{\infty}[f(x',t)W(x',x)-f(x,t)W(x,x')]\mathrm{d}x'$...
1
vote
3answers
776 views

General Definition of Steady State

According to many sources (including Wikipedia, Stephani&Kluge, D.J. Acheson) a steady state ist: In systems theory, a system in a steady state has numerous properties that are unchanging in ...
3
votes
1answer
220 views

$\delta$ differential notation

Various textbooks that I am currently consulting (including Spacecraft Dynamics and Control An Introduction - Anton H.J. De Ruiter | Christopher J. Damaren | James R. Forbes Section 1.4, page 32) use $...
0
votes
2answers
115 views

What is the difference in the two notation? [duplicate]

I have read in Zeemansky's physics $dQ=dU+pdV$ for first law of thermodynamics But when I came across another book of thermal physics,it says $δQ= dU +pdV$. So what us the difference ?
0
votes
1answer
511 views

Use of infinitesimals in physics [duplicate]

I want to ask about infinitesimals and non-standard analysis. In physics we always use $\mathrm dx,~\mathrm dv,~\mathrm dt$ etc. as infinitesimal quantities. When we deduce equations in physics, when ...
0
votes
1answer
351 views

Meaning the symbol, $W$ and $dW$

What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them. $dW$ here ISN'T power.
2
votes
1answer
529 views

Partial derivatives vs total derivatives in thermodynamics

The specific heat of a system is defined as $$C_z = T \left( \frac{\partial S}{\partial T} \right)_{z=\text{const}}$$ Sometimes however, I find the same definition, but with total derivatives ...
2
votes
1answer
313 views

Trying to understand the difference between $\Delta t$ and $dt$ [duplicate]

I'm trying to gain a more conceptual understanding of derivatives and would appreciate your feedback on this. Say I have a quantity, $x$, at time $t$. Now $x$ moves to a different location $x'$ in ...
2
votes
2answers
66 views

Is it reasonable and common to interpret $dt$ as a time point (a point in time)? [duplicate]

I heard some one talked about the instantaneous and average velocities. He was using $\Delta t$ to denote a time frame, $dt$ denote a time point. average velocities $\bar{v} = \dfrac{\Delta s}{\...
0
votes
3answers
93 views

What does $\Delta$ stand for? [duplicate]

Newton’s first law states that $\Delta v=0$ unless acted on by an external force, $F_{\mathrm{net}}\neq0$. Can someone explain to me what the $\Delta v$ symbol means?

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