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Questions tagged [calculus]

Calculus is the branch of mathematics which deals with the study of rate of change of quantities. This is usually divided into differential calculus and integral calculus which are concerned with derivatives and integrals respectively. DO NOT USE THIS TAG just because your question makes use of calculus.

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On Landaus&Lifshitz's derivation of the lagrangian of a free particle

I'm reading the first pages of Landaus&Lifshitz's Mechanics tome. I'm looking for some clarification on the derivation of the Lagrange function for the mechanical system composed of a single free ...
GeometriaDifferenziale's user avatar
1 vote
3 answers
78 views

What is the actual meaning of $dx$ in $W=-F.dx $, in work in thermodynamics?

what I want to ask is that the $dx$ in that formula is the displacement of piston or the displacement of the center of mass of the gas. also is there any situation where this clarity is useful.
Ujjwal's user avatar
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Why derivative of of internal energy with respect to temperature at constant volume is equal to partial derivative of same? [closed]

In statistical physics of particles by kadar it is written that derivative of internal energy with respect to temperature at constant volume is equal to partial derivative of internal energy with ...
Sravan Guruju's user avatar
-1 votes
1 answer
91 views

Speed is equal to distance divided by time but is this correct?

In this study https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9784821/, the distance the punch travelled from start to impact is 0.49 meters and the time taken from start of punch (that's it, they define ...
SnoopyKid's user avatar
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-1 votes
1 answer
70 views

What does the notation $d𝜏'$ mean?

$\text{I was studying helmotz theorem and saw this notation, what does it mean? How is d}\tau' \, \text{ different from d}\tau \text{?}$ From :- David J. Griffiths-Introduction to Electrodynamics-...
DocAi's user avatar
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-1 votes
1 answer
95 views

How to Find Trajectory of Particle?

Let’s say I have a particle, and I know all the forces acting on it at every position. (Let’s say the particle is in an electric/gravitational field to simplify the mathematics involved.) Now, is ...
V T Naveen Mugundh's user avatar
1 vote
1 answer
74 views

Magnetic Field on a point in a current carrying wire

Current carrying wire produces a magnetic field around it, we all know that. A circular wire carrying current produces a magnetic field around it due to the flow of electric charge. This phenomenon is ...
Gandalf73's user avatar
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0 answers
36 views

Trying to understand coordinate transformations [migrated]

So, I don't really understand why $\mathrm{d}x$ or generally any differential is equal to the sum of this differential over each one of the corresponding spherical coordinates times each spherical ...
Andronikos's user avatar
-3 votes
0 answers
50 views

Why cant we use $d(a^x)/dx = a^x \ln x$ to differentiate $y = 1^x$? [migrated]

Why cant we use d(a^x)/dx = a^x ln x to differentiate y = 1^x ? Is there any other way to differentiate it ?
Shinnaaan's user avatar
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When can I commute the 4-gradient and the "space-time" integral?

Let's say I have the following situation $$I = \dfrac{\partial}{\partial x^{\alpha}}\int e^{k_{\mu}x^{\mu}} \;d^4k$$ Would I be able to commute the integral and the partial derivative? If so, why is ...
clebbf's user avatar
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1 answer
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Material to Study the Definition, Algebra, and Use of Infinitesimals in Physics [closed]

This is going to be a rather general question about suggestions on best supplementary material to properly explain the use of infinitesimals (or differentials?) for the purposes of integration or ...
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1 answer
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Differentiation of a product of functions

If I have three (vector)functions, all dependent on different (complex)variables: \begin{equation} a = X^{\mu_1}(z_1, \bar{z}_1), b = X^{\mu_2}(z_2, \bar{z}_2), c= X^{\mu_3}(z_3, \bar{z}_3) \end{...
j_stoney's user avatar
2 votes
3 answers
69 views

$\int \vec{E} \cdot \vec{dA} = (E)(A)$?

I've seen this kind of simplification done very frequently in Gauss's law problems, assuming E is only radial and follows some "simple" geometry: $$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
JBatswani's user avatar
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1 answer
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What does this equation for density mean?

What does this equation for density mean? $$\rho = \lim_{\Delta V\to\varepsilon^3} \ \frac{\Delta m}{\Delta V}$$
sebbbb's user avatar
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1 answer
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Space-for-time Derivative Substitution in Solving for Elliptical Orbit

I am currently working on a simulation of the Newton's Cannonball thought experiment, in which a stone is launched horizontally from atop a tall mountain at a high speed (in the absence of air) and ...
Oscar Jaroker's user avatar
1 vote
0 answers
50 views

Integral of Theta function [closed]

I'm trying to compute the following integral, useful to calculate Amplitudes in String theory \begin{equation} \int \frac{d^2z}{\tau_2} \;\partial^2_z \log \vartheta_1\left(z\right) = - \frac{\pi}{\...
Roddy 's user avatar
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4 votes
1 answer
374 views

What are the odds of a rogue planet that enters into a galaxy reaching the black hole at the center of the galaxy?

I am wondering if anybody has ever calculated the odds of a rogue planet, which has been traveling through interstellar space and then enters into a galaxy, being able to travel all the way to the ...
user57467's user avatar
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1 vote
1 answer
38 views

Electric field at a point created by a charged object (derivation/integration process)

I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
1899DVX's user avatar
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0 answers
52 views

Partial derivative operator

It's mentioned in this paper that if $\partial^i \partial^j$ applied on an equation like: $$ x \delta_{ij} + (\nabla^2 \delta_{ij}- \partial_i \partial_j) y =0 $$ It yields a couple of equations: $$ ...
Dr. phy's user avatar
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2 answers
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Why is the differential form of Gauss's Law equivalent to the integral form?

I can understand the Differential form of Gauss's Law ∇⋅𝐄= $\frac{ρ}{ɛ_0}$ as saying that the source of electric field vectors or flow disperse(The divergence of the electric field) is equal to the ...
244529's user avatar
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0 votes
1 answer
75 views

In $a = dv/dt$, is $a$ the net acceleration? [closed]

While going through the calculus approach to accelerate, we have, $$a = dv/dt, $$ I think, here, v and a should be in the same axis, is my process correct? in a planar motion in two dimensions, it ...
sachin's user avatar
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-1 votes
3 answers
80 views

Proof that small change in temperature leads to small change in entropy

I have been trying to find a mathematical proof (or even from a reliable source) which verifies that/proves that: A small change in temperature leads to a small change in entropy. However, I was ...
PhysicsLover's user avatar
1 vote
1 answer
111 views

First law of thermodynamics: Can we always speak in terms of infinitesimal changes?

While reading lecture notes for the course on thermodynamics I have encountered some tiny details that seem extremely important for the understanding of the topic. However, something seems amiss so, I ...
Tomasz P's user avatar
0 votes
1 answer
93 views

Derivation of the state equation of a van der Waals gas. Can I invert the derivative to help me?

The state equation of a van der Waals gas is $$\left(P+\frac{a}{v^2}\right)(v-b)=RT$$ with $a,b$ and $R$ constant. Find $$\frac{\partial v}{\partial T}\bigg\rvert_P.$$ Finding $\frac{\partial v}{\...
Marcelo's user avatar
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1 vote
2 answers
122 views

Average velocity showing different results

I was solving a question, in which, a particle has travelled a distance $s$, with initial velocity $0$ and constant acceleration. So the equation of motion becomes, $$ v = a t \tag{1} $$ and $$ v = \...
Agent_A's user avatar
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1 vote
1 answer
18 views

Work done by electromagnetic forces when considering continous charge distributions

Here’s something that has always bothered me in my physics lectures. Suppose I want to calculate the work done by electromagnetic forces onto one charge $$ \begin{equation} dW = \vec{F} \cdot d\...
Jocobes's user avatar
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4 votes
0 answers
56 views

Energy in electric field of an electron?

I am just trying to get an intuition for the Griffiths equation no. 2.45, where work done to establish a field E is given by Say we want to solve it for electric field due to an electron (point-charge)...
SACHLEEN SINGH's user avatar
2 votes
2 answers
263 views

Vector potential of position field

Consider the position vector field $\vec{r}=(x,y,z)^T$. What would be a vector potential $\vec{A}$ for this field? I was thinking of something like $\vec{A}=(yz,zx,-xy)^T$, which gives $$\nabla\times ...
Riemann's user avatar
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2 answers
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Magnitude of Acceleration Vector when Speed is Constant

If I observe a change in direction of velocity, but not in speed: What does the acceleration vector look like? I am confused! The difference vector between two vectors of equal length A has a ...
Sylvia's user avatar
  • 123
0 votes
1 answer
70 views

Derivation of lagrange equation in classical mechanics

I'm currently working on classical mechanics and I am stuck in a part of the derivation of the lagrange equation with generalized coordinates. I just cant figure it out and don't know if it's just ...
Jan Oreel's user avatar
2 votes
1 answer
59 views

How to correctly integrate when acceleration is time dependent?

The problem is as follows: A ball moving in a straight line is experiencing acceleration $a(t)=kt$ until it arrives at a certain length $l$ when some time $t_f$ has passed. The initial speed and ...
Tensritu's user avatar
2 votes
2 answers
112 views

Consistency of perturbative theory when some of the first-order terms are smaller than second-order terms?

There is something that always puzzled me with perturbative approaches. To my understanding perturbative approaches are often qualified in terms of the order of the perturbation considered. For ...
Vincent's user avatar
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3 votes
4 answers
190 views

Is is true to say $F(x) = ma(x)$?

Considering the equation $F(t) = ma(t)$, I'm trying to figure out if the following is also always true: $$F(x(t)) = m\cdot a(x(t))$$ I.e.: $F$ as a function of $X$ (the position, which itself is a ...
Aviv Cohn's user avatar
  • 605
1 vote
3 answers
207 views

Are we allowed to cancel the units of a derivative?

Since the volume of a sphere $v(r)=\frac{4}{3} \pi r^{3} \left[m^{3}\right]$, its derivative relative to the radius is: $$ \frac{dv}{dr} =4\pi r^{2} \left[\frac{m^{3}}{m}\right] $$ Which is also a ...
Stanislav Bashkyrtsev's user avatar
2 votes
1 answer
282 views

Calculating the sag in a cable that has two different weights (two wires joined together)?

I'm familiar with the equation for the sag of a cable: $$x = \frac{wx(L-x)}{2T}$$ Where w = the weight per length, T = the tension and L = the length of the span between supports. I'm wondering if ...
am1234's user avatar
  • 29
-2 votes
2 answers
58 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 ...
Kenneth Mikolaichik's user avatar
0 votes
1 answer
54 views

Idea behind partial derivative with respect to space multiplied by length

Let $p$ be the pressure in the center of a volume. If $\delta\,x$ is the volume width, then the pressure on the wall can be expressed as $$p+\frac{\partial\,p}{\partial\,x}\frac{\delta\,x}{2}$$ My ...
Sylvia's user avatar
  • 123
0 votes
0 answers
43 views

Why is time taken to go around the Sun to cover a small fixed angle proportional to the square of the distance?

I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar ...
Neeladri Reddy's user avatar
0 votes
1 answer
84 views

Integral expansion of a ket [closed]

I'm taking my first quantum physics course and I've been seeing a lot of stuff like $|\psi\rangle = \int d\phi |\phi\rangle \langle \phi | \psi \rangle$ and $|\psi\rangle = \int d^3 r |r\rangle \...
JBatswani's user avatar
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0 votes
1 answer
48 views

Avg. velocity in plane polar coordinates

It's fairly easy to describe velocity, acceleration and displacement in plane polar coordinate system is the time interval is approaching to 0, but how can we calculate velocity, acceleration and ...
Manish's user avatar
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0 votes
0 answers
45 views

Force due to ring of charge [duplicate]

I am currently taking Physics II and have recently been focused on this problem: Suppose there is a ring of uniform linear charge density $\:\lambda\:$ and radius R and a point P at a height $\: z_{_\...
noneofyour's user avatar
0 votes
1 answer
82 views

Solutions of Laplace's equation for stream functions in cylindrical coordinates [closed]

I was reading Fluid Mechanics by Richard Fitzpatrick. Somewhere in the book, he tried to solve inviscid flow past a semi-infinite wedge https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node76....
Lohrasb's user avatar
  • 119
0 votes
3 answers
133 views

Is Jones calculus a "calculus" in the proper mathematical sense? [closed]

I've come to understand "calculus" as the mathematical study of continuous changes in a mathematical function or physical system. Differential and integral calculus are broad examples of ...
BenjaminDSmith's user avatar
-1 votes
1 answer
139 views

What does instantaneous velocity mean? [duplicate]

What does instantaneous velocity mean? on google it says "Instantaneous means something happens very quickly, in a single moment. It's similar to the meaning of "instant", but most ...
Intensed's user avatar
1 vote
1 answer
64 views

Integration to find force exerted by liquid on a tube

I was browsing PhysicsForums and I came across an interesting fluids question. I understood the method suggested to solve it, but I wanted to see if I could solve it through integral calculus. [...
zxen's user avatar
  • 63
0 votes
3 answers
116 views

Divergence of $H$ Maxwell equation

In the below screenshot from this paper (link below), why is the 2nd Maxwell equation ($\nabla \cdot H = 0$) not automatically satisfied when the 4th Maxwell equation is satisfied? I don't understand ...
photonica's user avatar
0 votes
1 answer
63 views

Given a distance, and velocity as a function of time, how do I find the time taken to travel the distance? [closed]

Given the velocity of a particle as a function of time V(t), and a distance between two points on a straight line (from point A to point B), I would like to find the time it will take the particle to ...
Aviv Cohn's user avatar
  • 605
2 votes
1 answer
48 views

Derivation of conserved current

Can someone give me some steps on showing the last line. From the line, $$-\int d^3x \space \epsilon_{abc} \space [ (\nabla^2\phi_b) \phi_c - m^2\phi_b\phi_c ] $$ I cannot actually see how could this ...
King Meruem's user avatar
11 votes
5 answers
3k views

In physics, when should one use and not use calculus?

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface ...
Dumb person 's user avatar
1 vote
2 answers
99 views

Why is density considered constant over a length $dz$ but not pressure?

When deriving the formula for hydrostatic equilibrium in the atmosphere, one usually considers a slab of air at altitude $z$, of thickness $dz$ and cross section $A$, and then writes $$A(P(z)-P(z+dz)) ...
aidaGoG's user avatar
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