Derivation Definition and 1000 Threads

Hi, in this link https://math.stackexchange.com/questions/2605752/proof-log-convex-implies-convexity , there is a theorem that labelled with yellow. I do not know the name of theorem and would like to know it's derivation. Could you please help me?

The famous Stirling’s approximation is ##N! \approx \sqrt{2\pi N}(N/e)^N## which becomes more accurate for larger N. (Although it’s surprisingly accurate for small values!) I have found a nice derivation of the formula, but there is one detail which bothers me. The derivation can be found...

Frankly, it is difficult for me to understand the derivation of mathematical equations that describe and explain the motion behavior of a gyroscope, particularly the reason why it spins in one direction, gravity tries to rotate it in a second direction, but it actually ends up turning in the...

I started studying Lagrangian mechanics, and the movement equation is like this: d/dt (d/dz') L - d/dz L = 0 if the movement is on the z axis. Now the problem is, let's say L = M(z')2/2 - Mgz. How do we derivate an expression depending of z with respect to z' and also , an expression depending...

Hi All, Is there any reference that shows in detail how to deduce the inductance effect of a coiled wire, starting from the magnetic influence of each current element ##i\, ds## on the others? Best wishes, DaTario

I am interested in the derivation of Schrödinger’s wave equation from the Klein Gordon equation. I have looked in Penfold’s ‘The Road to Reality’, the open University’s Quantum Mechanics books, Feynman’s lectures, the internet, but not found what I want. Everyone seems to take it as a given...

I am trying to derive the equation ##\vec{\Gamma} = \vec{m} \times \vec{B}##, where ##\vec{m} = I \vec{A}## is the magnetic moment, and ##\vec{A}## is normal to surface ##A##, from the Lorentz force law ##\mathrm{d}\vec{F} = I \vec{dl} \times \vec{B}##. For an arbitrary closed current loop ##C##...

A total derivative dU = (dU/dx)dx + (dU/dy)dy + (dU/dz)dz. I am unsure of how to use latex in the text boxes; so the terms in parenthesis should describe partial differentiations. My question is, where does this equation comes from?

The following are 3 equations of Planck's law or Planck's distribution function. Are they all correct? How do they derive from each other? Equation One: From page 512 of http://metronu.ulb.ac.be/npauly/art_2014_2015/shockley_1961.pdf We denote by Qs the number of quanta of frequency greater...

Hello! I am reading Schwarz's book on QFT and in chapter 17 he introduces the anomalous magnetic moment. I am not sure I understand a step in the derivation (from a mathematical point of view), when going from 17.23 to 17.24 (I attached a SS of it). I was able to get certain terms, but I am not...

From a previous thread, Nugatory: "If the answers already supplied are not enough for the original poster to work out for themself why x=vt+x'/γ, and not x=vt+γx′, is the correct expression, we can have another thread devoted to only that question." [SIZE=16px][FONT=PT Sans]Here it is. Either...

The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...

Homework Statement I am trying to improve my understanding of the Clebsch-Gordan coefficients. I am looking at page 5 of the following document https://courses.physics.illinois.edu/phys570/fa2013/chapter3.pdf Homework Equations I have derived the result for the I = 3/2 quadruplet but am...

Homework Statement Hookes Law gives: F = -kx. This is SHM. But I cannot see how to get to the sinusoidal expression from this. (In all the explanations, they cheat, and just introduce de novo Omega or Omega^2.) But how do you get to m. d2x/dt^2 = -x.(omega) ^2 Homework Equations F = -kx. m...

Homework Statement [please see attached photo] Homework Equations [please see attached photo] The Attempt at a Solution [please see attached photo] The issue for me starts with (but probably doesn't end with) replicating the velocity equation using the Conservation of Energy equations. Is...

If a beam of light is shot from a fast space ship, it travels a distance c*t1 according to their reference frame. The same beam of light seen from an outside observer goes at an angle and travels a distance c*t2. The distance the spaceship travels is equal to v*t2. Using the triangle made from...

In 'Introduction to Cosmology' by Barbara Ryden, there is an argument made using the first law of thermodynamics to derive the relation T(t) ∝ a(t)-1 on pages 29 and 30. MENTOR NOTE: removed copyrighted material. I've been able to work out all the omitted details up to 2.37, which gives the...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ... I am focused on Chapter 0: Complex Numbers and Continuous Functions ... and in particular on Section 1.3: Scalar Product and Absolute Value ... ... I need help in order to fully understand Remmert's derivation of the...

Not many people understood his proof in class, and the textbook's proof wasn't very clear so we went by with other derivations online. Then he filled half the midterm with his method, so I'm trying to understand how he did things. Looking back it seems very similar to the proofs we found online...

Homework Statement I have to simplify this beam form (equation 1) which simplifies to equation 2 and then finally to equation 3. Homework Equations equation 1: e^-ix((1-e^y)/(1-e^z)) where x = Beta*M_(1/2), y = beta*M, z= Beta equation 2: sin(M*Beta/2)/(sin(Beta/2)) equation 3...

Homework Statement Derive the formula for the Doppler effect for a receiver traveling at an angle theta away from a planar source Homework EquationsThe Attempt at a Solution [/B] I thought that we can assume that the wavelength has two components ##λ_x## and ##λ_y## where ##λ_x = ct+vtcosθ##...

https://arxiv.org/abs/1411.6992 They derive the born rule from the MWI. Is this circular?

Homework Statement a)recall that electric potential is a scalar quantity. For a circular ring of radius, R', carrying charge, Q, what is the electric potential at a height,y, above the center of the ring? b)Use your above answer to determine the electric potential at a height,y, above the...

Homework Statement ok this is not a homework but i am confused by the derivation of ## f = \nabla (m . B)## both start out with ##\vec B(r) \approx \vec B_0 + (\vec r' . \nabla)\vec B|_0 ... \\ f = \iiint_{v'} \vec J( r') \times (\vec r' . \nabla)\vec B|_0 ## where prime is body coordinates and...

I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that...

In my textbook there is an explanation of a derivation of D'Alembert equation for pressure waves. (##\frac{\partial^2 y}{\partial x^2}=\frac{\rho}{\beta}\frac{\partial^2 y}{\partial t^2}##) I put the picture (the only one I found on internet) but I'll call ##y_1 ,y_2## as ##\psi_1,\psi_2## and...

Hi, I learned about how PE = U=kq1q2/r is the electrical potential energy for the system. It is found by taking the integral of electrical force and dr from infinity to the point of location we are interested in. So that is the intregral(F*dr) from r=inf to r=ro. My question is that do I...

Hello PF, first of all I don't know where to put this post as it's not exactly a homework question but a clarification question for a project. I'm going through the derivation of the effective permeability of two stacked medias, given the polarization of an incoming EM wave but I'm stuck at the...

Hello everyone, I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation? Thank you

In this derivation: https://cpb-us-e1.wpmucdn.com/sites.northwestern.edu/dist/8/1599/files/2017/06/taylor_series-14rhgdo.pdf they assume in equation (8) that x >> a in order to use the Taylor Expansion because a/x has difficult behavior. Why does that assumption work? Meaning, why can we...

From what I have read the twin paradox can be resolved with the Rindler metric and without the need to bring in general relativity. Special relativity will suffice. But how does the Rindler metric get derived in the context of a constant accelerating reference frame. I haven't seen anything in...

Homework Statement Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2). Homework EquationsThe Attempt at a Solution My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign...

Hello! This is my first post on this forum, so make sure to tell me if I am doing something wrong :) I was trying to derive the Lorentz factor today, and I used the following page as a guide. The top answer by Jimmy360 is what I followed...

Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model. I have attached my attempt to this post. It is quite long and...

I have a question about a very specific step in the derivation of Euler-Lagrangian. Sorry if it seems simple and trivial. I present the question in the course of the derivation. Given: \begin{equation} \begin{split} F &=\int_{x_a}^{x_b} g(f,f_x,x) dx \end{split} \end{equation} Thus...

I'm trying to figure out how the finite volume version of Lax-Wendroff scheme is derived. Here is the PDE and Lax-Wendfroff scheme, assume initial conditions are given: $$u=\text{function of x,t}\\\hat{u}=\frac{1}{\Delta x}\int_{x_{i-1/2}}^{x_{i+1/2}}u\thinspace dx \text{ (the average flux...

I would be grateful if some one would consider my following thought and indicate to me the likely mistakes, which I cannot do. Following the paper “Why the Riemann Curvature Tensor needs twenty independent components” by David Meldgin UC Davis 2011, I understand that with a coordinates...

Hi, I'm trying to grasp the standard derivation of the quantum Zeno effect. But my calculus is limited. I would love some assistance! Schroedinger evolution tells us that the state at time t, given the initial state at time t=0, is: |\psi_t\rangle = e^{-i H t} |\psi_0 \rangle We can then...

For a beam above between two columns and bars are yield and hinging.. the formula to get the probable shear or vpr (from statics) is V= M(+) + M(-) /ln I guess it is derived from V * ln = M(+) + M(-) First of all. Why is the shear only present when it is hinging and not before (I'm talking...

Starting from the definition of energy levels ##e_n## and occupations ##a_n## and the conditions ##\sum_n a_n = N## (2.2) and ##\sum_n a_n e_n = E## (2.3) where ##N## and ##E## are fixed I'm trying to find the distribution which extremizes the Shannon entropy. Using the frequency ##f_n=a_n/N##...

Can somebody please post the derivation of the ABC magnetic field components whose magnetic field components in the three cartesian directions(B1, B2, B3) are given by the following: B1=A*sin(z)+C*cos(y) B2=B*sin(x)+A*cos(z) B3=C*sin(y)+B*cos(x)

My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...

I set a small project for myself to design a controller for a rocket, which moves a mass around to shift the center of mass, in order to steer a rocket. The picture shows a simplified model of a rocket plus a movable mass. , shown is a rod for the rocket, and a mass for the controller. there...

Homework Statement is dx/dy= x/y if yes can i use it always Homework Equations for example in a circle dA/dtheta=A/360The Attempt at a Solution if its right sometimes what are the conditions of using it

Hello, I am currently taking a course on general relativity with the book "General Relativity: An introduction for physicists" by M.P. Hobson. I am a having a hard time understanding the derivation presented for the Einstein equations. The book states that Einstein proposed the following...

I have just started learning the Special Theory of Relativity. While deriving, I am facing some problems. I obviously have made some kind of mistake while using the equations... What is wrong if I don't use the time transformation equation in Event #2?

Hey, I tried to construct the derivation of the integral C with respect to Y: $$ \frac{\partial C}{\partial Y} = ? $$ $$ C = \frac{2}{\pi} \int_0^{\infty} Re(d(\alpha) \frac{exp(-i \cdot ln(f))}{i \alpha}) d \alpha $$ with $$d(\alpha) = exp(i \alpha (b + ln(Y)) - u) \cdot exp(v(\alpha) + z...

Hello, here's a derivation for one of the equations for Uniform Accelerated Motion (UAM). I like it because it's far more concise than the algebra version. Question though: is there any kind of meaningful interpretation of ds/dv (which starts everything off in step 1)? Thank you!

I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q}} = \frac{1}{\sqrt{V}} \sum_{\overrightarrow{k}}...

Hey guys , my lecturer introduced a new concept with reference to the commutation of two operators.He claimed that if two commutators commute then they can be simultaneously measured.I can clearly see how this works.He then went on and state if they don't commute they can't simultaneously be...