deriving Definition and 1000 Threads

Deriving Expectations (i.e. means) I'm looking at my Introduction to Econometrics book and trying to figure out the derivations in the 2nd Chapter. First, E(Y^{2}) = \sigma^{2}_{Y}+\mu^{2}_{Y} The derivation goes like this: E(Y^{2}) = E{[(Y - \mu_{Y})+ \mu_{Y}]^{2}} = E[(Y- \mu_{Y})^2] +...

I'm trying to get from the magnetic vector potential \vec{A}(\vec{x},t) = \frac{1}{\sqrt{\mathcal{V}}}\sum_{\vec{k},\alpha=1,2}(c_{\vec{k}\alpha}(t) \vec{u}_{\vec{k}\alpha}(\vec{x}) + c.c.) where c_{\vec{k}\alpha}(t) = c_{\vec{k}\alpha}(0) e^{-i\omega_{\vec{k}\alpha}t}...

An extremely elementary question but... Lets say we had a spaceship sitting on Earth under the influence of gravity. Light travels from the ship's floor to the ceiling. An observer 'A' stands near the ceiling. Hence the light loses gravitational potential energy, and therefore decreases...

Homework Statement The De Broglie Wavelength of any object in motion is given by \lambda=\frac{h}{P} where h is Planck's constant and P is the body's momentum. for heavy masses this wavelength is too small to be observed, nevertheless it is still there... I have seen a derivation for this...

[SOLVED] Deriving the head-on collision equation in terms of v2' and v1' I think I'm having an algebra issue here, but how is the momentum equation (where v2=0): m1(v1-v1')=m2v2' combined with v1+v1'=v2' to give: v2' = v1 [ 2m1/(m1+m2)] and v1' = v1 [(m1-m2)/(m1+m2)] I'm...

Homework Statement Integrate e^{iz^2} around the contour C to obtain the Fresnel integrals: \int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4} The contour consists of three parts: z = x, 0 \le x \le R z = Re^{i\theta}, 0 \le \theta \le \pi/4 z =...

Homework Statement Starting from the equations of conservation of mass and momentum for an inviscid compressible gas, \frac{\partial \rho}{\partial t} + \bigtriangledown . (\rho {\bf u}) = 0 \rho ( \frac{\partial {\bf u}}{\partial t} + ({\bf u}. \bigtriangledown){\bf u}) = \bigtriangledown...

Something has always bothered me about the way the de Broglie relation is derived and I've never seen anyone address this, so I'm hoping someone here can. As I understand it, the derivation begins with two of Einstein's equations: E=hf, and E=pc. E=hf was experimentally obtained by Einstein...

Homework Statement Derive the equation for angular frequency for simple harmonic motion of a spring. Homework Equations Derive omega = sqrt(k/m) from F = -kx (sorry i don't know how to use notation) The Attempt at a Solution I asked my teacher how to do this, and he used some...

This is probably more Calculus than it is physics. The voltage at a point X produced by a uniformly charged rod is V = (Ke*Q/l)*[ln(l+sqr(l^2+a^2))-ln(a)], in which point X is right above the left end of the rod by a distance a, l is the rod's length, Q is the charge of the rod, and Ke as the...

If the Ricci-scalar R is constant for a given spatial hypersurface, then the curvature of that region should be homogenous and isotropic, right? A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry): d\sigma^2 =...

Homework Statement I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage.. 2. Homework Equations / attempt Let: c = velocity of light. v = the velocity as observed from where time t is measured. D = distance AB. t = time light occupies to...

Homework Statement Derive... x(t)=(exp^(-\zeta\omegat))*(a1(exp^(i\omegasqrt(1-\zeta^2)*t)))+a2(exp^(-i\omegasqrt(1-\zeta^2)*t)))) into x(t)=(exp^(-\zeta\omegat))*(A sin (\omega*t + \varphi)) Homework Equations n/a The Attempt at a Solution I've managed to get x(t) =...

Hello, First post. Thank you for letting me be a part of the discussion. My question is, can the Law of Conservation of Energy, http://upload.wikimedia.org/math/2/7/3/273abc16486177bf6cc4c8ec4a4a5fc9.png, be derived using E=MC2. I understand that the E=MC2 can be derived using the LoCE...

I have been trying to show that the Einstein ring radius R_e = 2[GMx(L-x)/(Lc^2)]^1/2 to no avail. can someone who knows this show me, or at least point out the direction. I have a strong hunch that i'll have to use the light bending formula for small angles
delta_phi = 4GM/(bc^2), and...

Homework Statement I found on Wikipedia the formula for energy density of an electric field in a vacuum to be U = \frac{1}{2}\epsilon_0 E^2. I was wondering if someone could point me in the right direction to figure out how this was derived. Homework Equations The Attempt at...

Ok, so I'm really at a loss as to how to do this. I can prove the formula by just using determinants, but I don't really know how to do manipulations with the levi-civita symbol. Here's what I have so far: (\vec{B} \times \vec{C})_{i} = \epsilon_{ijk}(B_{j}C_{k})\vec{e_{i}} And I'm...

Homework Statement I have a problem that asks to derive the doppler effect for the two different cases of a moving observer and a moving source. Homework Equations I should get f' = f*(v +/- vo)/(v +/- vs) as my general equation, where f' is the observed frequency and f is the...

Projectile Motion! Please Help! Homework Statement The acceleration due to gravity can be measured by firing a projectile upward and measuring the time it takes to pass two given points in both directions. The figure below is a plot of height versus time and shows that the time the...

Homework Statement There is a uniform electric field E, and a uniform magnetic field B in space. A particle of mass m, and charge q, at the origin is released from rest at t=0. The only acting force on the body is the Lorentz force. Derive the trajectory of the particle for t>=0. Homework...

Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how? Thanks

Homework Statement Derive the Laplace transform of the following functions, using first principles 3d) u(t - T) \} = 0, \ t<T \ (= 1, t>T) 3e) f(t) = e^{-a(t-T)}u(t-T) Homework Equations see above The Attempt at a Solution I know I need to derive the transform using by integration...

I would like to derive a relation for shear stress on a conical bore shaped fluid element. Essentially, I have flow going through a converging nozzle. I know variables in this include length of the nozzle, inlet and outlet diameters and pressures and nozzle angle. I've done a force balance on...

Hi, I have a quick question about a derivation that has annoyed me all day. I am trying to prove, from the definition of \otimes that: T(\theta,\tau)=T^{i\alpha}(e_i,f_\alpha) Where \theta \in V^* and \tau \in W^* T: V^* \times W^* \mapsto \mathbb{R} and where V has basis e_i and W has basis...

Homework Statement Derive the moment of inertia for a solid sphere with a uniform mass Homework Equations I= \sum mr^{2} The Attempt at a Solution I decided to change everything to polar coordinates. Since the polar coordinate substitution is \int\int\int_{v} Fr^{2}sin(\phi)drd\phi d\theta...

I have a bit difficulties deriving the equation V in =Vout * R2/(R1+R2) Because I can't see a closed loop here Can someone help with this Thx

How would I go about deriving the cooridinate numbers of both ions in rock salt, and, how could I account for the differences in lattice enthalpy between the following; LiCl (861 kJ/mole) - NaCl (787) LiCl - LiF (1046) LiCl - MgO (3850) Cheers.

Given tanA=y/x.....(1) Can anyone tell me how you get the following relations: =>sinA=ay/sqrt(x^2+y^2).....(2) =>cosA=ax/sqrt(x^2+y^2)....(3) where a=(+/-)1 I know tanA=sinA/cosA and sin^2(A)+cos^2(A)=1...and I can see by substituting (2) and (3) into (1) it works, but I really...

Homework Statement Suppose we lived in a matter-dominated, critical-density universe. The matter density rho of such a universe changes with time t as a power of t. Derive the value of the exponent n in the following equation: Homework Equations rho = At^n where A = constant

Homework Statement We have a straight wire with radius R. What is the magnetic induction through point A at a distance of r? In other words, derive the equation B=\frac{\mu_{0}i}{2\pi r} by using d\vec{B}=\frac{\mu_{0}i}{4\pi r^2}(d\vec{l} \times \vec{u_{r}}) Homework Equations...

Homework Statement Deriv µs = tan θ For when a block is put on a wooden plank and the plank is lifted at one side. Homework Equations tan = sin/cos Ff = µFn The Attempt at a Solution Ff = µFn -mgsinθ= µ (-mgcosθ) µ =(-mgsinθ) /(-mgcosθ) µ = tan θ Where i am confused is why Ff...

when we derive the wave equation for a an o0ne dimensional wave moving at constant speed we assume that the wave move losslessly that is a plot of \psi(x,t) with x at any time t is same to the extent that one can be obtained from the other by translation. similarly what are the assumptions when...

Dear all, I am new here and hope that I write this in the right place. ;-) I am seeking help in deriving Ji's Sum Rule, which tells you that the second moment of the nucleon's GPDs equals the total angular momentum of the quarks. E.g. in Diehl, hep-ph/0307382, Sect. 3.6. The step where...

Homework Statement A circular curve of radius R in a new highway is designed so that a car traveling at speed v can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will...

I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...

Homework Statement x(t)= (7.00m/s)t + (7.00m/s^2)t^2 - (2.00m/s^3)t^3 a) find the expression for the velocity as a function of time. b) plot the graphs of the position, velocity and acceleration as accleration vs time for the interval given. c) At what time(s) btw t=0 and t= 3.00...

Homework Statement I am wondering if someone could give me some insight on how the following infinite series was derived: P_e = \sum_{-\infty}^\infty (1/2)^{2|n|} = -1 + 2 \sum_{n=0}^\infty (1/2)^{2n} = 5/3 Homework Equations See above The Attempt at a Solution I think the -1...

Homework Statement Automotive engineers refer to the time rate change of acceleration as the Jerk. Assuem an object moves in 1 dimention such that it's Jerk is constant. a) determine expressions for it's 1. acceleration ax(t) 2. velocity vx(t) 3. position x(t) given initial...

I'm looking for a good book for graduate students that indicates how one can obtain a (classical) potential from a tree-level Feynman process. For example, how can one go from the S-matrix of e.g. Compton scattering and derive the Coulomb potential. Any help would be appreciated.

I was going through the derivation of the Taylors series in my book (Engineering Mathematics by Jaggi & Mathur), and there was one step that escaped me. They proved that the derivative of f(x+h) is the same wrt h and wrt (x+h). If someone could explain that, Id be really grateful.

Homework Statement Okay, this lab has had me stumped for the last few hours. This is our first lab for AP Physics BC. Problem: Determine the position vector that describes the locatino of the water that is launched by a drinking fountain. Your position vector needs to be in unit vector...

How do you derive the equation for the launch angle using the range and peak equations? This isn't a homework problem but something i want to know for my own general knowledge for solving physics problems. Is there a site that has physics equations solved for different variables? Hyperphysics is...

Homework Statement Derive (v_f)^2 = (v_i)^2 +2ad Homework Equations (v_f)^2 = (v_i)^2 + 2ad (v_f) = (v_i) + at d = (v_i)t + \frac{1}{2}at^2 The Attempt at a Solution I have attempted to replace the variables with others from other kinematic equations such as v_f = v_i + at...

How do we come to 4.pi.r^2?

hi frenz i want to how to derive mathematical relation between dependent(output) and independent(input) variables when i know the relation between them at few samples. cud someone help me out? thanks in advance

Homework Statement I need to derive some equation that are on the paper "does the inertia of a body depend on it's energy content". http://www.fourmilab.ch/etexts/einstein/E_mc2/www/" I just don't know where to start and if someone can point me to the right direction, it will be so much...

For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...

Homework Statement Basically I am given an image showing a test charge tied to a string where there is the ball is stationary. I need to use the fact that there is no net force on the ball to derive an equation for the electrostatic force in terms of g, the angle, and the mass of the ball...

Two ladders, one red, and the other green, are 2 and 3m long respectively. The base of the red ladder is resting on the side of a narrow hallway and leaning on the wall of the other side of the hallway. The green ladder is doing the same, but on the opposite side, such that the two ladders cross...

I am having a huge problem with understanding the derivation of velocity profiles for these type of problems. The one i am having the most difficulty is the flow of oil going down vertically along the surface of a glass rod. Where p=900 kg/m^3 and u=120 mPa's. How do I start this problem?