Derivation Definition and 1000 Threads

Hi, I am following this : https://en.wikipedia.org/wiki/Geodesics_in_general_relativity and all is good except how do we get ## \delta g_{uv}=\partial_{\alpha}g_{uv}\delta x^{\alpha}## Many thanks

In the derivation given in Goldstein's book it is given I can't understand from where it comes. It's not at all trivial for me but it's presented as if it's trivial.

Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...

Hey All, Question about hydraulics. Can't seem to find anyone videos or material to walk me through how to get the formula deltaF = rho*g*(A1+A2)d2 Any takers? My book states: The conclusion is conservation of evergy. Work is done on the liquid by a small force pushing the liquid through a...

What is wrong with the simple localised geometric derivation of the Euler Lagrange equation. As opposed to the standard derivation that Lagrange provided. Sorry I haven't mastered writing mathematically using latex. I will have a look at this over the next few days. More clarification. I...

I was reading about the classical Klein-Gordon propagator here: https://en.wikipedia.org/wiki/Propagator#Relativistic_propagators Basically they are looking for ##G##, that solves the equation $$(\square _{x}+m^{2})G(x,y)=-\delta (x-y).$$ So they take the Fourier transform to get...

Does anyone know the heuristic derivation of this formula? $$R=r_{0} \cdot A^{\frac{1}{3}}$$ with ##R## the atomic nucleus, ##r_0## the radius of a nucleon (proton or neutron) and ##A## the number of nucleons. I know that there is a sperimental derivation, but I would find a theoretic/heuristic...

Hello, I am trying to work through attached paper, deriving from equation 2.2 to 2.4. I am not familiar with the notation. If I try and get the integral of inside the <> brackets, I end up with a different eqn 2.4. I need some maths help here :) Any help would be greatly appreciated...

When considering bound states of potential energy that tends to zero at large ##r##, my book arrives in $$\frac{d^2}{dr^2} u_{E} = \kappa^2 u \ \ \ \ \kappa^2 \equiv -2mE/ \hbar^2 > 0 \ \ \ \ r \rightarrow \infty$$ from the differential equation satisfied by ##u_{E} \equiv R_{El} (r) / r##...

Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...

Exact differential of a scalar function f takes the form of ∇f⋅dr=Σ∂ifdxi (where dr is a vector) f:R->Rnand I am not sure why this equation is valid in the sense that if we integrate the equation, ∫∇f⋅dr=∫{Σ∂ifdxi} ∫df=∫{Σ∂ifdxi} the above equation is true because integration is a linear...

I'm reading Modern Particle Physics by Mark Thomson and watching Susskind's lecture on QM. In Thompson's book, equation (2.41) the wavefunction is expressed in terms of complete set of states of the unperturbed Hamiltonian as \Psi(\textbf{x}, t) = \sum_{k} c_k(t)\phi_k(\textbf{x})e^{-iE_kt}...

Why do they introduce the partition function. I have seen it in the derivation of the Boltzmann distribution. But I don't know the physical significance of it here? And how do they get to (L.11) after that? I get everything until L.7. Including L.7. The rest of the proof is here just in case...

Homework Statement I understand the derivation it showed that included the sin (15.7 in the image) I just don't understand the following (15.8 in the image). Does "t" get pulled out of the equation? If so what do we derive for then? Does it become 0? If so, it would remain 0 and sin(0) is just...

In this paper (https://arxiv.org/abs/astro-ph/0603302) the authors derive the field equations for f(R) gravity considering a spherically symmetric and static metric. Now the Ricci scalar only depends on r so you could write f(R(r)) = g(r) for some g. However what it seems the authors have done...

Homework Statement Hello I have this circle with the equation : [/B] (x-a)^2+(y-b)^2=r^2 I want to find dy/dx for it 2. Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...

Homework Statement I am trying to derive the dipole-dipole interaction derivation, which is: U=(-p1p2/4πϵ_0) (1/z^3) ((2cosθ_1cosθ_2)− (sinθ_1sinθ_2cosζ)) Where p1 and p21 are the two dipole moments, r is the distance between two dipoles on the y axis, θ_1 and θ_2 are the angles between the...

Hello PhysicsForum, There is something I don't get at the end of this course notes PDF file. In the last section, titled "Comoving distance and redshift", which I have copied below, we have a short derivation of the comoving distance and redshift relation. Almost all is well, the only thing...

In the derivation of Euler-Lagrange equation, when differentiating S with respect to α, there is a step: $$\frac{\partial f(Y,Y',x)}{\partial\alpha}=\frac{\partial f}{\partial y}\frac{\partial y}{\partial\alpha}+\frac{\partial f}{\partial y'}\frac{\partial y'}{\partial\alpha}$$ Where $$ Y =...

Take the first three terms of Navier Stoke equation: $$\rho \cdot \left ( v_{x}\cdot \frac{\partial \vec{v}}{\partial x} + v_{y}\cdot \frac{\partial \vec{v}}{\partial y} + v_{z}\cdot \frac{\partial \vec{v}}{\partial z}\right )$$ Define the length ##v## of the velocity vector field...

Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L =...

Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...

Hi all, Sorry if this is the wrong section to post this. For some time, I have wanted to derive the Laplacian in spherical coordinates for myself using what some people call the "brute force" method. I knew it would take several sheets of paper and could quickly become disorganized, so I...

I know that deriving y = bεax gives dy/dx = abεax, I also know that the inverse of dx/dy equals dy/dx, so how come I don't get dy/dx = abεax when I do the following: ln(y) = ln(bεax) = ax ln(bε) -> x = ln(y)/(a ln(bε)) -> dx/dy = 1/(ay ln(bε)) -> dy/dx = ay ln(bε) = abεax ln(bε) ≠ abεax What...

I went through an example question that showed me how to solve the question but I'm not sure if I've misunderstood something or if they did a mistake. Question: Derivate y = (1/ax)ax ln(y) = ln( (1/ax)ax ) = ax( ln(1) - ln(ax) ) = -ax ln(ax) (1/y)(dy/dx) = -ax * ax ln(a) - a * ln(ax) dy/dx =...

I´m able to derive Bernoulli equation from the force bilance of the flowing element (particle): dm\cdot \left (\frac{D \vec{v}}{D \tau } \right )_{flowing particle}=\vec{dF}_{g}+\vec{dF}_{p} where dFg is the gravitational force acting on the particle, dFp is the pressure force acting on the...

I have encountered this paper "Curie Wiess model of the quantum measurement process". https://arxiv.org/abs/cond-mat/0203460 Another work by the same authors is "Understanding quantum measurement from the solution of dynamical models" https://arxiv.org/abs/1107.2138 I am still evaluating the...

I've been following the derivations in the following video up until that point. I don't quite understand why does it imply that μ*ε=1/c^2. Thanks.

Dear all, I am working on a car-accident prediction model. I found the following equations here that worked in my model. However, I could not figure out how the equations were derived. Could anyone help me in understanding the derivation of the mintime and mindist equations (Steps 3 and 5...

I was looking for the derivation of stoke's drag F=6πηrv But I'm only getting the derivation by dimensional analysis. Can anyone please provide it's real derivation? I'll really appreciate it.

My question is:why is small work done,dW taken as F.dx instead of x.dF because integrating the latter should also give the same result(taking x out of the integral and integrating dF gives x (F) ).Visualising this integration graphically seems to suggest the same. Similar is the case with...

Homework Statement Inscribe in a given cone, the height h of which is equal to the radius r of the base, a cylinder (c) whose total area is a maximum. Radius of cylinder is rc and height of cylinder is hc. Homework Equations A = 2πrchc + 2πrc2 The Attempt at a Solution r = h ∴ hc = r - rc A =...

I've managed to derive the form of Reynolds transport theorem as a bilance of linear momentum of the system: \left (\frac{\vec{\mathrm{d} p}}{\mathrm{d} \tau} \right )_{system}=\frac{\mathrm{d} }{\mathrm{d} x}(\int_{V}^{ }\vec{v}\cdot \rho dV)+\int_{A}^{ }\vec{a}dm+\int_{A}^{ }\vec{v}\cdot \rho...

My notes state that the method is constructed based on the idea: yk+1=yk+∫f(x,y)dx where the integral is taken from xk to xk+1 We can estimate the integral by considering ∫f(x)dx (from xk to xk+1) =c0fk+c1fk-1 To simplify the equation, we move xk to the origin such that ∫f(x)dx (from 0 to h)...

While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index. But where's...

Please, help here people. Im reading this article Wave Optics in Gravitational Lensing (T. T. Nakamura, 1999) . In the article start work with \begin{equation} (\nabla ^2 +\omega)\tilde\phi = 4\omega^2U\tilde\phi \end{equation} where $$\tilde\phi = F(\vec r)\tilde\phi_{0}(r)$$. Using...

hi, I am looking for a proof of weibull distribution, I have searched a lot but nothing is reasonable for the proof, so ıs there derivation of this distribution ? What is the origin of this distribution ?

I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...

Homework Statement I'm trying to find the output voltage ripple of a buck converter by using just the waveforms and the inductor ripple. Homework Equations [/B] I know that the answer is supposed to be D(1-D)Vin/(16*L*C*f^2) but I keep getting D(1-D)Vin/(8*L*C*f^2)The equations I end up...

Hi all. I ended up to this section in K&K (2nd edition, but with 1st is the same) when they derive the wobbling motion of a simple body in torque-free precession. [see the attached file] Equations 8.23 and 8.24 are integrated into 8.25[a|b], but I think signs are wrong. Shouldn't be negative...

Can someone explain to me (or point me towards a source) how is the Lorenz Gauge derived? I am reading the Griffiths book and from what I understand we can do the transformation ##A' = A + \nabla \lambda## and at the same time ##V' = V - \frac{\partial \lambda}{\partial t}## and B and E remain...

Hello. I was having a hard time determining how the formula for the average value of the waveform can be achieved. I've read that the ave since the waveform is symmetric is (Imin+Imax)/2. I want to know how to derive it using calculus. Thanks.

Homework Statement After a long time, an inductor is disconnected quickly from the battery and then attatched to a resistor. Homework Equations V = Ldi/dt V = ir The Attempt at a Solution KVL: voltage across inductor - voltage across resistor = 0 Ldi/dt - ir = 0 di/i = rdt/L ln|i| from i(t)...

Hello, I have a question regarding the first equation above. it says dui=ai*dr=ai*aj*duj but I wonder how. (sorry I omitted vector notation because I don't know how to put them on) if dui=ai*dr=ai*aj*duj is true, then dr=aj*duj |dr|*rhat=|aj|*duj*ajhat where lim |dr|,|duj|->0 which means...

I came across this website and I intend to find out more about work done by gravity and derivation of gravitational potential energy (Sorry, the thread name is too long, so I abbreviate it as G.P.E.) Ok, here is the problem. I am quite confused with the calculation of work done against gravity...

Homework Statement For some reason it is not letting me add the image here, here is the link to the question: http://imgur.com/a/3DLWM The part I'm stuck on is the last part. Basically, the question is to obtain the following equation for the entropy of vaporisation using the Redlich-Kwong...

Homework Statement Hi, I am reading this book called, Introduction to Corporate Finance, by Berk, Demarzo, Harford (second edition). In it they try to explain how to calculate the number of periods in a loan payment formula. Authors give the following equation. $$ 0 =PV + PMT \times...

Let's say we have a path Length AC. Point A transmits a signal at Ptransmit. From Friis' Path Loss formula: (assumming Gain for receiver and transmitter antennae are 1.) ##P_{received} = P_{transmit} (\frac{λ}{4π* LengthAC})^2## ,when point C contains the receiver. What if I divided this into...

I have a question stating to derive the functions x |-> f_1(x)=x^3 and f_2(x)=thirdrootof(x) on their domains of definition based on the asymptotic relative condition number KR = KR(f,x). I'm not sure where to start with this question, I'm not sure if I even understand it. Do I find the...

In lectures, I learned that in first order perturbation, \hat{H}_0 term cancels with E_0 term because \hat{H}_0 is Hermitian. What property does Hermitian operators hold that cancels with the unperturbed energy?