All Questions
9 questions
-2
votes
2
answers
62
views
Can the different differentiation notations be equated and do they have an integral definition? [closed]
Are these all equivalent and is there an extension of this to other notation?
Does anyone have a clear and concise chart equating the different notation dialects?
I am also curious if there are more ...
0
votes
0
answers
44
views
Does this particular notation for derivatives imply anything in particular? [duplicate]
In some physics textbooks (and in those of other sciences that use physics, like soil science), I've seen some derivatives written as:
$$\frac{\delta f}{\delta t} $$
Which is a bit strange. Does this ...
- 3,623
0
votes
1
answer
57
views
What does this vertical line notation mean?
Here is the definition of the Noether momentum in my script.
$$I = \left.\frac{\partial L}{\partial \dot{x}} \frac{d x}{d \alpha} \right|_{\alpha=0} = \frac{\partial L}{\partial \dot{x}} = m \dot{x} = ...
- 85
0
votes
0
answers
80
views
Why is cancellation of differnetial not allowed here?
This is about cancelation of differentials .I am learning basics of tesnor from "Mathematical Methods " by Boas. There I encountered this epression which author says are equal. $$ \frac{\...
- 128
12
votes
6
answers
3k
views
Using differentials in physics [duplicate]
I was lately wondering about the use of differentials in physics. I mean, usually $dx$ is thought of as a small increment in $x$, but does this have any rigorous meaning mathematically.
Doubts started ...
- 139
1
vote
4
answers
420
views
What do $\nabla$ and $\frac{d }{d t}$ mean when they are by themselves?
In QM and QFT, I have seen some equations where they have just the derivative and/or the gradient without specifying what it is acting on.
Taken from wiki.
This does not make sense to me since I ...
- 2,042
0
votes
1
answer
74
views
Analogous notation to $\nabla$ but for gradient with respect to $\vec{k}$ not $\vec{x}$
$\nabla = \frac{\partial}{\partial x_i}$ so $\nabla F = (\frac{\partial F}{\partial x}, \frac{\partial F}{\partial y}, \frac{\partial F}{\partial z})$.
However, is there a similar equalivalent notion ...
- 2,654
-1
votes
1
answer
111
views
What is $\delta t$? [duplicate]
I'm confused whether it's difference between two times (i.e final and initial) or it represents very small time.
- 17
0
votes
1
answer
2k
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 ...
- 41