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3
votes
1answer
53 views

How to set up line integral of electric field? Confused over notation

In multivariable calculus the line integrals was parameterized and denoted: $$ \int_C \mathbf{F} \bullet \, d\mathbf{r}=\int_D\mathbf{F}(\mathbf{r}(t)) \bullet \frac{d \mathbf{r}(t)}{dt} \, dt $$ ...
-4
votes
0answers
34 views

Modulus in Calculus? [migrated]

Does Modulus function has any effect during differentiation and integration of a quantity? For example: Let two velocities be: $$ v_1= (t-2) m/s $$ and $$ v_2=|t-2|m/s $$ If we differentiate them ...
0
votes
3answers
108 views

Can we have a physics by using other mathematics except calculus? [closed]

We (I) always have been said that we don't need to real values, we just need to differences. For example, $\mathrm du=C_v\mathrm dT$ and $\Delta u=\int_{T_1}^{T_2}C_v\mathrm dT$. So, I have some ...
5
votes
2answers
162 views

Calculating Intensity/Strength of Vibration with 3DOF

I want to calculate the intensity/strength of vibration at a given location. I have measured the acceleration at this location, using an accelerometer. So my measures look for example like: ...
1
vote
0answers
11 views

Proof from Calculus 1 [migrated]

Last days, from going into a website of the university of Pisa, I found an exercise given in the previous exams, in 1999. The problem was like: Given a continuous function f in R, and which ...
0
votes
1answer
28 views

How to calculate orbit of a sphere around a bigger one in microgravity?

I don't have any knowledge in physics, but in a world building related question, I need to know how can I calculate the orbit or the distance in each point of the orbit around a spherical object in ...
3
votes
3answers
93 views

Why we use differential element to get general form? [closed]

When we study any physical system we use differential element to get an equation then integrate over specific period to get a general form. Why we don't get directly a general form without ...
-1
votes
1answer
65 views

What does $f(v)d^3v$ mean?

I am reading the derivation of Langmuir's Evaporation Equation. The author writes: That cylinder contains a volume $dA(vdt)cosθ$ and contains vapor molecules of the designated speed in the ...
0
votes
1answer
38 views

How to treat the units of measure when taking a derivative?

I've had a doubt for a long time: when I'm taking the derivative, of a function for example, how should I treat the units of measurement? For example, if I'm taking the derivative of: $$S\,[{\rm m}]=...
0
votes
4answers
89 views

Explain $\Delta x = v_0t + \tfrac{1}{2}gt^2$ please? [duplicate]

$g = \Delta v/t$, so $\Delta v = gt$. $v = v_0 + \Delta v$, so $v = v_0 + gt$. So if $\Delta x = vt$, then $\Delta x$ should be $v_0t + gt$. Why the $\tfrac{1}{2}gt^2$? I'm really confused, so this ...
1
vote
4answers
56 views

Area under and slope of the motion graphs

I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph. I'm confused that area is a 2 dimensional concept and it ...
4
votes
2answers
586 views

Check dimensions of the integral of a function

I and a colleague are arguing about the dimensions of: $$\int_0^x f(x) dx $$ in this particular case $[f(x)]=m^2/s^3$ and $[x]=m$. Does it follow that $[\int_0^x f(x) dx]=m^2/s^3$ or $[\int_0^x f(x)...
1
vote
1answer
51 views

Inverse metric in Newtonian limit of GR

I am reading Carroll's book. So looking at the Newtonian limit we write $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$ where $h_{\mu\nu}$ is some small perturbation. He says that because $g^{\mu\nu}g_{\nu\...
0
votes
1answer
105 views

Bridges between maths and physics: the $\tau=2\pi$ constant [closed]

[disclaimer: I am not a math or a CS major, this is probably an easy question for most people on Physics SE.] I just read the tau manifesto explaining - according to its author - the various ...
0
votes
0answers
23 views

Spivak for a soon to be undergrad. physics student [duplicate]

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
0
votes
0answers
45 views

Difference between integral and differential physical laws [duplicate]

Why is integral and differential physical laws both used? I read that integral is global and differential is local. Could you tell me something about it?
0
votes
1answer
67 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
46 views

Vector Integrals: can I take out the vector outside of the integral?

Question: Solution: The notation used is: $(x,y,z)$ is for rectangular coordinates, $(\rho,\varphi,z)$ for cylindrical coordinates and $(r,\theta,\varphi)$ for spherical coordinates. ${ { \hat ...
0
votes
1answer
28 views

Equations of motion acceleration doubt

So i was going through some text today morning. Where it said $$ a = \frac{vdv}{dx} $$ So they then went on to, $$ vdv = adx \\ \implies \int vdv = \int adx$$ But,I am very certain acceleration is ...
1
vote
3answers
47 views

Equations of motion derivation doubt

I just started on learning how to derive the equations of motion using calculus. This is my first time and I have a basic doubt. So $v = \large{\frac{dx}{dt}}$ Then, $dx = v dt $ What does this ...
2
votes
0answers
69 views

What is the variation of pressure in rotating fluids(in accordance to the question in the image)? [closed]

This is an interesting question that I came across. Please see attachment. It is a multiple answer type question. My answer was B and D. I have attached my derivation for this problem. I want to know ...
5
votes
3answers
940 views

What are the differences between the differential and integral forms of (e.g. Maxwell's) equations?

I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell: How to know where to apply each way? Excuse ...
4
votes
3answers
218 views

Is $\dfrac{dx}{dt}$ a fraction or not?

I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that $\dfrac{dx}{dt}$ ...
0
votes
1answer
37 views

Differential Operator

I am trying to understand the following expression \begin{eqnarray} e^{-ik.x}D_{\mu}D^{\mu}e^{ik.x} & = & e^{-ik.x}(i\partial_{\mu}+A_{\mu})(i\partial^{\mu}+A^{\mu})e^{ik.x}\\ & = & e^{...
1
vote
0answers
38 views

Finding the exponent of $\lambda$ in Wien's displacement law

I am reading this paper on a short history of the $T^4$ radiation law. In particular, on page 5, By assuming that the wavelength of radiation emitted by a molecule was a function only of its ...
0
votes
2answers
79 views

Is the motion of a particle non-analytic?

I really can't understand what happens during the time $t(0)$ to $t(0+dt)$ in the following crackpot arguement: A particle is at rest (in an ideal frictionless world) until $t(0)$. So every order ...
0
votes
0answers
33 views

How to derive velocity, distance from a changing acceleration?

I'm making a electronic device that is out of the scope of this site, but essentially it gives me acceleration readings every X microseconds. Given these samples of acceleration, how can I find out ...
0
votes
3answers
42 views

Flux - Scalar Multiplication in Integral?

No textbook and website seems to answer this so here is my question: When we have a scalar flux: I understand that you take the scalar product of the vectors. And I understand the need for using an ...
0
votes
3answers
79 views

A relationship between entropy and temperature

I tried deriving a formula relating entropy (not change in entropy, but entropy itself) to temperature. I’ve only seen two equations really relating to entropy thus far, and only one of them includes ...
1
vote
1answer
39 views

Quick question - infinitesimals proofs [duplicate]

In a few of my courses in mechanics certain statements/equations have been proved by assuming that two infinitesimals multiplied by each other are zero. For instance in the equation : $dx + dy + dx^2 ...
2
votes
1answer
52 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct ...
1
vote
0answers
25 views

Help to verify (numerically) invariant Haar measure on unitary group

Sorry if this question is not appropriate for the forum. From the paper http://gemma.ujf.cas.cz/~brauner/files/Haar_measure.pdf I am interested to understand and verify equation (3). Can anyone please ...
1
vote
1answer
98 views

What is the meaning of $\mathrm{d}^4k$ in this integral?

From Gerardus 't Hooft's Nobel Lecture, December 8, 1999, he states the following equation (2.1): $$ \int \mathrm{d}^4k \frac{\operatorname{Pol}(k_{\mu})}{(k^2+m^2)\bigl((k+q)^2+m^2\bigr)} = \infty ...
0
votes
1answer
57 views

If the integral is zero when is the integrand zero? [closed]

Using Stoke's theorem we prove that the curl of the Electric field vanishes. This would be possible only if the integrand is zero when the integral is zero.
0
votes
1answer
92 views

Fallacious derivation of the rocket equation

Consider a rocket in free space of initial mass (including fuel) of $m_0$ using up/ejecting fuel at a constant rate $r$ (mass per time). That means that at time $t$ the rocket has mass $m=m_0-rt$. The ...
0
votes
1answer
92 views

Does the complex conjugate of a vector have the same direction as the vector?

Looking at reflected and transmitted optic waves, the $\overset{\rightharpoonup }{E}_t$ vector is always perpendicular to $\overset{\rightharpoonup }{k}_t$ (as seen in the attached image). So $\...
0
votes
1answer
76 views

Calculating Potential Energy

I'm familiar with the potential energy equation, but I'm concerned with the value of 'g' in it. I know that, at sea level, earth's gravitational acceleration is 9.81 m/s/s. So I know that within the ...
0
votes
1answer
39 views

The dot product integral in the proof of the Parallel axis theorem

The first picture is a question about proving the Parallel axis theorem and the second is the solution. I have no problem with the solution except for the part which says that $$ \int 2\vec h \cdot \...
0
votes
1answer
47 views

Differential derivation based upon time and space confusion

I have been doing a lot of derivations recently involving heat transfer. I was attempting to derive heat accumulation in a differential element based upon inflow and outflow as well as thermodynamic ...
3
votes
4answers
122 views

Intuitive explanation of the half in the $\frac{1}{2}at^2$ distance equation?

The full equation $$ Xf = X_o + V_o t + \frac{at^2}{2} $$ is integrated from the velocity function (which was integrated from constant acceleration function), right? The problem is, I can't seem to ...
1
vote
0answers
40 views

3 Particle problem with a difference

Please read this completely, it is not the typical question you expect. 3 particles are at the corners of an equilateral triangle with side a. Assume that particle 1 is at (0,0), particle 2 is at (a,...
2
votes
2answers
59 views

Why dont you take derivative of force in definition of power ? P=F.v

The derivative of work is $\bf F\cdot v .$ $$P(t)= \frac{\mathrm dW}{\mathrm dt}= \mathbf{F\cdot v}=-\frac{\mathrm dU}{\mathrm dt}\;.$$ But why not $$(\mathrm d(\mathbf F)/\mathrm dx)\cdot \mathbf x ...
1
vote
0answers
28 views

Is there a way to find the optimal angle to launch an object to get maximum distance when there is an initial height? (Projectile motion) [duplicate]

I know that the optimal angle to launch an object at ground level is 45 degrees; however, i want to know that if there is anyway to get the optimal angle to launch an object to get the maximum ...
1
vote
1answer
119 views

What does $L^2(S^1,\mu_H)$ mean?

It's a Hilbert space, $\mu_H$ stands for the Haar measure on $U(1)$, but what does $S^1$ mean? I found it in one of my quantum mechanics books which approaches from a very 'mathematical' way.
1
vote
1answer
37 views

How to model terminal velocity as a function of gravitational acceleration?

Taking the most simplistic form of terminal velocity, $v=\sqrt{\frac{mg}{c}}$ I want to try and derive an equation that models the velocity as g changes in height.. Because obviously the terminal ...
0
votes
0answers
13 views

Calculate distance with variable acceleration [duplicate]

I know the time and I know the force that acts horizontally on a particle. The problem is that the force is F=k(D-V), where k and D are constants. So at the beginning where the particle has zero ...
0
votes
3answers
436 views

How to prove the average velocity formula without calculus

I often see the formula: $$ \overline v = \frac {v + v_0}{2} $$ in physics textbooks, to describe the average velocity for an object moving with constant acceleration. This formula is often ...
1
vote
0answers
52 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
1
vote
2answers
96 views

Divergence-free vector field on a non-simply connected domain

We know that divergence-free vector fields are themselves curls of vector fields on simply connected domains. I want to construct a counterexample in the case the domain is not simply connected. So ...
0
votes
2answers
231 views

Calculus versus Algebraic Kinematic Equations

Deriving the first equation of motion using either algebra or calculus you get the exact same thing, but my knowledge was that you use integral calculus in physics when you have a varying variable, ...