Derivation Definition and 1000 Threads

My derivation of Taylor expansion. Hope someone struggling with it gets use!

Any advice on my derivation layout?

Homework Statement For an s-polarized wave (E and B fields are orthogonal to the plane of incidence) passing from medium to medium 2, I'm not understanding a minus sign. The matching conditions are ##\hat n \times (\vec E_2 - \vec E_1)=\vec 0## and ##\hat n \times (\vec H_2 - \vec H_1 )=\vec...

HI people, I was trying to derive the stefan-boltzman law from the planc's formula, I kind of got stuck with an integral $$ \int_{0}^{\infty} \frac{x^3}{e^x -1} dx $$ I tried simplifying it with $$ \int_{0}^{\infty} x^3 e^{-x} \sum_{n=0}^{\infty} e^{-nx} dx $$ Now I don't know what to do...

I always see the contribution of semiclassical scattering to the Bloch equations for a two-level system justified heuristically, using Fermi's Golden Rule to calculate the scattering rates. The resulting time evolution of the density matrix is clearly in the Lindblad form, but is it possible to...

Homework Statement I'm looking at an E&M textbook - "Time-Harmonic Electromagnetic Fields". They state: "A more general ##x ## polarized field is one consisting of waves traveling in opposite directions with unequal amplitudes - i.e : (1) $$ E_{x} = Ae^{-jkz} +Ce^{jkz}$$ Let ## A ## and...

A comparison of corresponding parts of these two similar isosceles triangles yields velocity triangle displacement triangle where |-vo| = |vf| = v In a small time interval Δt, the arc length s → c. Okay, so I got this from Physics LAB, and I don't understand the last statement that...

Hi, I'm watching a talk about Archimedes Law of the lever, and I was wondering: Does anyone know how the formula d=w/2w/b-a) was derived from the lecture drawing at 9.00 min in? The speaker just skips the algebraic derivation.

Homework Statement Derive the following result : \phi_k=-C_1(k)\frac{\dot{H}(t)}{H(t)} . Homework Equations \phi_k=C_1(k)\Bigg(1-\frac{H}{a}\int\limits^{t}a(t)dt\Bigg) a(t)= a(t_i)\exp\Bigg(H_i(t-t_i)+\dot{H}_i\frac{(t^2-t_i^2)}{2}\Bigg) The Attempt at a Solution So I stuck a(t) into...

Homework Statement In a book I find the following derivation: \int (J \cdot \nabla ) \frac{\bf{r} - \bf{r}'}{|\bf{r} - \bf{r}'|^3} d^3\mathbf{r'}= -\sum_{i=1}^3 \int J_i \frac{\partial}{\partial r_i'} \frac{\bf{r} - \bf{r}'}{|\bf{r} - \bf{r}'|^3} d^3\mathbf{r'} \\ = -\sum_{i=1}^3 \int J_i...

I am trying to understand the formula's for Gravitational Radiation. At one point in the derivation, every source I have seen comes up with Kirchhoff's Formula but they never derive it. They always just say its a well known result from Electromagnetic Radiation. I have been able to determine...

I'm looking for a derivation of the Einstein-Cartan Equations from varying the Einstein-Hilbert Action. I've looked around the internet but can't seem to find one, so if anyone knows of a pdf or book reference that goes through the derivation, that would help a lot. The wikipedia page for...

I have a question concerning the tangent space. Consider a manifold Mn and take Mn to be ℝn with the Euclidean metric for the purposes of this question. The directional derivative of a function in the direction of a vector v is (a) vf = ∑ vi(∂f/∂xi) where the sum runs from 1 to n. The...

On page 12 of Zee's QFT in a nutshell, he rewrites an integral from dirac notation to a mixture of schrodinger/dirac My question is, since , what happened to the integrals, and shouldn't there be four wave functions instead of two? I tried writing out the integrals explicitly, thinking maybe...

Homework Statement A lever with one end on a pivot point, a point mass on the lever's shaft with a certain arm length (d), it is also the only relevant mass body (m). A torque (Tauapp.) is applied to the lever, an angular acceleration (alpha) transpired. Find the relationship between the force...

the equation (P+a(n/V)^2)(V-nb)=nRT was derived in this manner: The pressure of a real gas is affected by intermolecular forces and so the a(n/V)^2 term must be added to the measured pressure to obtain the ideal pressure where Pmeasured+a(n/V)^2=Pideal On the other hand when they explained...

Hi All, I have problem in understanding one step in the derivation of the time dependent Schrodinger Equation. Please see attached file page 2 (marked in red). Most grateful if someone can help! Peter Yu (This is from Quantum Mechanics The Theoretical Minimum Page 99-102)

derive f distribution as x1 and x2 are independent random variables having a chi-square distribution with n1 and n2 degrees of freedom.. aslo mgf and find raw moments ... and finds its mean and variance.?prove it ?help me guys?

hi, i am a lillte confused why the equation for hookes law is 1/(2pi*c)*sqrt(k/m_reduced)? where does c come from? http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf - slide 8. also, is there any particular reason why we use reduced mass?

Hi dear people , Hello I waw studying super position of two Sound Waves , traveling in same medium with same frequency , same wavelength and same amplitude while differing in phase . quick derivation : Wave 1 displacement y1= A sin (kx-vt ) and wave 2 displacement y2= A sin (kx-vt-phase...

First of all, I am sorry if this is in the wrong subforum; I'm not sure if astrodynamics should be under astronomy. The post is also fairly long. My problem is that in my derivation of the center of mass of a binary system, I get a conflicting result for the distances of the center of mass to...

I would like to know how can I derive the double, half, product to sum, and sum to product identities of trigonometry using simple algebraic means. And which books (which I prefer) should I pickup at the library on this subject to actually learn these derivations? Or at the very least some...

eifphysics submitted a new PF Insights post A Partial "Derivation" of Gauss's Law Continue reading the Original PF Insights Post.

Hi, Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.

Hi. A very long problem brought me to a derivative in the form \frac{\mathrm{d}f(x)}{\mathrm{d}g(x)} I'm assuming that \mathrm{d}g(x)=\left(\frac{\mathrm{d}g(x)}{\mathrm{d}x}\right)\mathrm{d}x So, is it correct to say that...

My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor : L = 1/(4π^2 . f^2 . C) Here, f = different resonant frequencies, C = capacitance of the capacitor in the LC...

is there any derivation of Newton second law?

Mentor note: fixed formulas so they get displayed properly If we take the K-G eqn and the following term for the wave function $$( \partial^2 + \frac{m^{2}c^{2}}{\hbar^{2}})\Psi =0 \\\\\Psi = Re^{-i\omega t + i k_{i}x_{i}}$$We worked through to this ##\hbar \omega = \pm \sqrt{\hbar^{2}...

Hi I am doing some exam revision for an EM class and I'm trying to understand a few things about this derivation. Specifically in equation 18.23 why do we not consider the derivative of the four velocity i.e ##\partial^{\alpha}U^\beta## Then going from 18.23 to 18.25 why is...

I have attached a photo of a page from a book that I am studying. The author is showing a derivation of E(ave) = kT However, I can't follow this derivation. He says that you need to use integration by substitution and I am OK with that. But when he actually does the substitution it looks...

I want to know how coloumbs constant was derived without using gausses law

I'm really happy about every hint! Homework Statement There is a ball on hight h which is dropped on a table. With every Impact the ball loses velocity v by a factor a<1. I Need to Show the following: The time T after the ball stopps bouncing is: T = \frac{1+a}{1-a} (\frac{2h}{g})^\frac{1}{2}...

I am working to use the artificial potential field method for path planning of mobile robot; actually I found in one of references the following description about this method: the artificial potential field method uses a scalar function called the potential function. This function has two...

Whenever I try searching on how coloumbs law is derived Gauss's law is always used,for this reason when I search for Gauss's law it is always derived from coloumbs law :frown:.could you guys guys help me out by telling me which camfirst and how it was derived Coloumbs law- F=Q1Q2/r2ε Gauss's...

I've seen derivations for c=E/B and c=1/√μ0ε0, but I don't seem to get the directions right. i.e. I end up with a negative sign in one of the equations. The derivations I've seen do not use vector calculus. One derivation I've seen is in http://Derivation[/PLAIN] of Electromagnetic Waves from...

From Apostol's Calculus Volume I, "Area as a Set Function" 1. Homework Statement : Right triangular regions are measurable because they are constructed from the intersection of two rectangles. Prove that all triangular regions are measurable and have an area of the product of one-half, their...

Homework Statement The sun experiences a vertical gravitation acceleration of g=-4πGρz, where ρ is the density of the disk of our Galaxy. a) Assuming that d2z/dt2=-kz, express k in terms of ρ and G. b) Find the general expression for z and w=dz/dt as a function of time. c) If the total mass...

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]##ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2}))## [2] ##ds^{2}=dt^{2}-R^{2}(t)g_{ij}dx^{i}dx^{j}## where...

I'm trying to prove that ##\sqrt{-g}\bigtriangledown_{\mu}v^{\mu}=\partial_{\mu}(\sqrt{-g}v^{\mu}) ## So i have ##\sqrt{-g}\bigtriangledown_{\mu}v^{\mu}=\sqrt{-g}(\partial_{\mu}v^{mu}+\Gamma^{\mu}_{\mu \alpha}v^{\alpha}) ## by just expanding out the definition of the covariant derivative...

d=vt+1/2at^2 Derive me this formula please... When I do I get 1/2(vt+at^2)...i know that I'm doing a mistake by not considering the initial velocity... So how do I correct it?

Using R = ρL/A, I am trying to get this formula, which is the change in resistance due to change in length, area, and resistivity. ΔR = (∂R/∂L)ΔL + (∂R/∂A)ΔA + (∂R/∂ρ)Δρ I understand the above conceptually, but I am confused about why we are multiplying by terms ΔL, ΔA, and Δρ. Intuitively, I...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] I am following a lecture on carrier concentration and I got to the point where the instructor said that for homework, derive the carrier concentration equation ni, which...

Hello, It's my first question here. So I'll try to give as much as information as I know Actually I am stuck with a problem of centre of mass derivation of a triangle with its base on the X axis and symmetric about it. The base is b and height is H As far as I know I have to imagine it as a...

Homework Statement This is not really a homework problem but I wanted to figure out how to derive the equation for a strained eye which is $$ M= (N/f) $$ where N is the object distance from the normal near point, and f is the focal length of a magnifying glass. But then, this is for a relaxed...

Here is a screenshot from a page from a textbook that explains how to derive the ideal gas law: In the third bold line, I don't understand how "time" in force = (change of momentum)/(time) is equal to 2x/u (the time it takes for the particle to travel to the opposite face and back again) -- I...

Hi, The integrals in the image are well-known, but we are not allowed to use them in the test. I have tried to prove them using changing variable t, but I didn't succeed. Can you show me the way?

Homework Statement I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you...

during these first few steps, where did the constants in front of the integrals come from for a_0,a_n, b_n? http://i.imgur.com/rky0mdf.png (wasn't sure whether to post this as a separate topic or back with the other one)

Hello! Dr. David Tong, in his statistical physics notes, derives the Boltzmann distribution in the following manner. He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R)...

Hi, I'm trying to wrap my head around the derivation of the wave equation and wave speed. For starters I'm looking at the derviation done on this site: http://www.animations.physics.unsw.edu.au/jw/wave_equation_speed.htm I could maybe explain what I understand at this point Given a string with...