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2 answers
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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 ...
Kenneth Mikolaichik's user avatar
2 votes
1 answer
355 views

$\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do? [closed]

I'm trying to teach myself Smoothed Particle Hydrodynamics. Unfortunately, my background is in electronics, so the Navier Stokes equations are somewhat alien to me, as is vector calculus. The video I'...
ScottishTapWater's user avatar
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} = ...
Lambda's user avatar
  • 85
1 vote
1 answer
288 views

Question on how to make product rule for differentiation consistent with operators? [duplicate]

By the product rule for differentiation:$$\frac{\partial(\hat A\psi)}{\partial x}=\left(\frac{\partial\hat A}{\partial x}\right)\psi+\hat A\left(\frac{\partial\psi}{\partial x}\right)\tag{1}$$ Where $\...
a Fish in Dirac Sea's user avatar
2 votes
1 answer
89 views

Does the expression "$𝑑𝑠^2$..." mean the same thing as "$\Delta 𝑠^2$... "?

I reviewed this question but sometimes I'm unsure about delta ($\Delta$) versus differential ($d$) notation. Does the expression "$ds^2=-c^2dt^2+a^2(t)[dr^2 + S_k^2(r)d\Omega^2 ]$" mean the ...
bblohowiak's user avatar
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{\...
mum's user avatar
  • 128
0 votes
2 answers
204 views

Physical meaning of the exterior derivative of the first law of thermodynamics

We know, $$ dU = d \overline{q} - d \overline{W}.$$ suppose we took the exterior derivative on both sides, then: $$ 0= d( d \overline{q}) - d( d \overline{W})$$ This means, $$ d^2 \overline{q} = d^2 \...
Brian's user avatar
  • 8,040
0 votes
1 answer
34 views

Help decipher the notation said to denote a common pattern in various branches of science in Prelude to Mathematics by W. W. Sawyer

In Section 1.2 - Nature's Favorite Pattern? (excerpted below) of Prelude to Mathematics by W. W. Sawyer (1982), he said mathematicians used the notation $\nabla^2 V$ to denote a pattern that occurs &...
reflectionalist's user avatar
0 votes
2 answers
326 views

Is there any difference in superscript and subscript notation in finite difference method

Is there any difference in superscript and subscript notation in the finite difference method? I see the same paper use (superscript for $x$ and superscript for $y$ notation) and (subscript for x and ...
Abinash's user avatar
2 votes
1 answer
87 views

How to express the elementary work definition as an explicit functional expression [duplicate]

My assumption here is that in the definition of elementary work : $dW = F ds$ symbol $d$ represents a differential. But a differential implies a function : $dy =_{df} d[f(x)] = f'(x) \Delta x = f'(...
Floridus Floridi's user avatar
0 votes
1 answer
305 views

What does an "elementary value $\delta$ of a quantity" mean?

In page-11 of I.E irodov Fundamental laws of mechanics, some notation used in the book is introduced. There, it is said that $\delta$ denotes the elementary value of a quantity but what exactly does ...
Brian's user avatar
  • 8,040
3 votes
2 answers
133 views

Is this notation inconsistent? If not, can some explain why not?

Im working through a textbook section on particle kinematics. An example given is relating vertical velocity to horizontal velocity and states: $y$ has a constant velocity of $10 \ \rm [m/s]$ $y=(0....
RoRo's user avatar
  • 31
1 vote
1 answer
101 views

What does the $d$ mean in metric tensor calculations?

In many metric calculations, like the Schwartzschild metric, we see formulas like $d^2X / dt^2$ and many other formulas with a $d$ in them. You'd be surprised that I've been looking for months to ...
foolishmuse's user avatar
  • 4,855
-1 votes
2 answers
603 views

What does $d$ stand for in this formula?

Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am ...
ShinyWhaleFood's user avatar
1 vote
1 answer
77 views

Interpretation of Variation Notes

I would like an explanation to how this Lagragian partial derivative was taken (eq. 3). This probably is more suited for the math Stack Exchange, however this is for a physics course which is why I am ...
Tom's user avatar
  • 15
0 votes
3 answers
624 views

Showing the equivalence between the chain rule's Leibniz and Lagrange Notations

This may seem more math related but this question crossed my mind as I was reading the derivation of the Euler-Lagrange Equation. In math, we were introduced to the Lagrange notation of the derivative ...
Shinobu's user avatar
  • 97
-2 votes
3 answers
104 views

Changing derivative to difference quotient

Can differential be changed to Delta or difference? In high school education, in the acceleration section of Newton's formula 2, acceleration is a change velocity (velocity difference) divided by a ...
Herza Ryo's user avatar
1 vote
0 answers
285 views

Why do they specify the differential of Work using an lowercase delta $\delta W$, instead of $dW$ [duplicate]

I was curious, why do they specify the differential of Work using an lowercase delta symbol $\delta$ as in "$\delta W$", instead of using a $d$, as in $dW$. For example: $$\delta W=\vec{F} ...
Bill Moore's user avatar
2 votes
1 answer
253 views

Abuse of Calculus [duplicate]

I'm following Professor R. Shankar's Fundamentals of Physics course on YouTube. There I saw him doing manipulations of Calculus I never saw before. Here it goes, $$\newcommand\deriv[2]{\frac{\mathrm ...
ARahman's user avatar
  • 21
2 votes
1 answer
3k 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 ...
Steven's user avatar
  • 197
-1 votes
1 answer
651 views

What is difference between $d\vec{l}$ and $\vec{dl}$? [closed]

What is difference between $d\vec{l}$ and $\vec{dl}$? $d$ means differential as usual.
Magneto's user avatar
  • 15
6 votes
2 answers
5k views

What does $(\mathbf{u}\cdot\nabla)\mathbf{u}$ mean in the Navier-Stokes equation?

I am studying the Navier-Stokes equations and I have the equation in the form: $$\rho \dfrac{\partial{\mathbf{u}}}{\partial{t}} + \rho (\mathbf{u}\cdot\nabla)\mathbf{u} - \mu\nabla^2\mathbf{u} + \...
Ayisha Mahmudova's user avatar
0 votes
3 answers
577 views

What is meant by $dy/y$?

Consider the language in the following example: What is meant by $dg$ and $dR$, and also by $dg/g$? Why does $dR/R=-2/100$ (negative for shrinks)? Is $4\%$ unity change? I mean $dg/g=4\%$ or $dg=...
john.David's user avatar
2 votes
1 answer
5k views

Two different meanings of $\nabla$ with subscript?

I am trying to understand the meaning of $\nabla$ when it appears with subscript. I have found two separate Physics SE answers that imply different meanings. The notation $\vec \nabla_B$ means ...
gen-ℤ ready to perish's user avatar
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 ...
Nesar's user avatar
  • 41
3 votes
2 answers
5k views

Feynman's subscript notation

Consider this vector calculus identity: $$ \mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) \...
bc87's user avatar
  • 163