Derive Definition and 591 Threads

If I know the mean and standard deviation, but I don't have an original data set, is it possible to reverse calculate a data set that has this known mean and std dev? Is there an excel function I could use to do this easily? I know there could be multiple correct datasets and that's fine, I'm...

How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it...

Hello everybody, Sorry to ask you something that may be easy for you but I'm stuck. For example I have 2 images (size 2056x2056). One image of reference and the other is the same rotated from -90degrees. Using a program with keypoints, it gives me a transform matrix : a=2.056884522e+03...

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...

Homework Statement Given an NxN symetric tri-diagonal matrix, derive the recursion relation for the characteristic polynomial Pn(λ) Homework Equations Pn(λ) = |A -λI | Pn(λ) = (An,n - λ)Pn-1(λ) - A2n,n-1Pn-2(λ) The Attempt at a Solution This was easy to do by induction, but I am always...

Can the Heisenberg's Gamma Ray Microscope thought experiment derive the Uncertainty Principle precisely? Most derivations I find, the uncertainty is roughly 2h, whereas the uncertainty principle is "hbar over 2". Is there anywhere where there is more precise calculations to obtain "hbar over 2"...

Does anyone know the proof of joint moment generating functions for bivariate normal distributions? M_x,y (s,t)= E(e^(xs+yt))

Homework Statement A positive charge +q is located at the point x= 0, y = -a and a negative charge -q is located at the point x=0, y=a (a) Derive an expression for the potential at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the...

Hello, I noticed that the solution of a homogeneous linear second order DE can be interpreted as the kernel of a linear transformation. It can also be easily shown that the general solution, Ygeneral, of a nonhomogenous DE is given by: Ygeneral = Yhomogeneous + Yparticular My question: Is it...

Homework Statement ##x=r\sin\theta\cos\phi,\,\,\,\,\,y=r\sin\theta\sin\phi,\,\,\,\,\,z=r\cos\theta## ##\hat{x}=\sin\theta\cos\phi\,\hat{r}+\cos\theta\cos\phi\,\hat{\theta}-\sin\phi\,\hat{\phi}## ##\hat{y}=\sin\theta\sin\phi\,\hat{r}+\cos\theta\sin\phi\,\hat{\theta}+\cos\phi\,\hat{\phi}##...

Sorry to bring this question up again. @aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as: $$...

Homework Statement Derive the infinitesimal rotation operator around the z-axis. Homework Equations My book gives this equation (which I follow) with epsilon the infinitesimal rotation angle: $$ \hat{R}(\epsilon) \psi(r,\theta, \phi) = \psi(r,\theta, \phi - \epsilon) $$ but I just don't get...

Derive an exact formula (solve the recurrence definition) for the following recursive sequence: $s_n = 2_{s_n-1} - s_{n-2}$ where $n \ge 2$, and $s_0 = 4$, $s_1 = 1$. So I saw someone solving this by making it a differential equation or something? How would you do that? should I do let...

I'm trying to figure out how to derive the equations for Energy from the differential equation corresponding to the (simple and damped) harmonic oscillator. Please note that I don't want to start with the expressions for kinetic and potential energy, I want to derive them. The references that I...

How do i go about deriving a general eqn for the nth term of a sequence provided an eqn of the sum to the nth term is given in terms of n?

question: I came across a question which said: Derive the equation for kinetic energy of a body of mass m and velocity v. What do they mean? Attempt: I actually just wrote that by work energy theorem diff. in KE = work done so Fx = KE $$ max = m \frac {v²-u²}{2x} x = ½mv² - ½mu² $$ each of...

THIS THREAD HAS BEEN MOVED FROM ANOTHER FORUM BECAUSE IT IS HOMEWORK. BUT THERE IS NO TEMPLATE. Hi everyone, The problem gives that a particle moves in a circle with angular velocity ω. I know that r×ω=v, which is the velocity of the particle. However, I am told to differentiate and find τ=Iα...

T=m[1]m[2]g/(m1+m2)

Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...

Homework Statement I am reading Mathematical Concepts of Quantum Mechanics (Stephen J. Gustafson, Israel Michael Sigal. Second edition). The book would like to find an evolution equation which would lead to the Hamilton-Jacobi equation $$\frac{\partial S}{\partial t}=-h(x, \nabla S) $$ in the...

Homework Statement For a single molecule, derive the internal energy U = 3/2kBT In terms of the partition function Z, F = -kBTlnZ Where Z = V(aT)3/2 Homework Equations Thermodynamic identity: δF = -SδT - pδV p = kBT/V S = kB[ln(Z) + 3/2]The Attempt at a Solution U = F + TS δU = δF +...

In Serway physics, ampere derived Ampere's law(integral B dot ds=uI) with work done on the magnetic charge by magnetic field.(similear with E dot ds) Without using vector calculus, how can derive Ampere's law from Biot-Savart law?

Homework Statement Hi I need to know the derivation of the equation HT2 = delta HT1 + delta Cp delta T and I'm really unsure of where to find this. Does anyone know the derivation of this relationship? C represents the the specific heat of the substance in question. H represents enthalpy...

I have been recently working with Schwarzschild's solution: ds2= - (1- (2GM/rc2))c2dt2 + dr2/(1-2GM/rc2) + r2(dθ2 + sin2(θ)d∅2) Now, when deriving the various general relativistic tensors for this metric such as the Ricci tensor, I found the calculations to be painfully tedious and monstrous...

Hello there, I want to derive ##U(\theta) ## for electric dipole placed in uniforum electric field $\vec{E} = E\vec{e}_x$ where E is constant. I define the dipole moment as $p = qd$, where $d$ is the distance from the two I write $\mathm{d}W = p\,E\sin\theta \mathrm{d}\theta =...

Hi Guys, please help me. how can i derive the primitive vector of copper oxide (I)? basically this is cuprous oxide having a cubic crystal structure but since it has oxygen in it the directions and magnitude of primitive vector are far different compare to basic cubic structure. also please help...

Homework Statement density matrix : ρ(t)=0.5+0.5*a(t)⋅σ (a is a 3 dimensional vector and σ is paul victor) H=-μ*σ⋅B (B is a three dimensional magnetic field ) and also assume that in t=0 , ρ(0)=0.5+0.5*a(0)⋅σ whats is the motion equation of a(t)? Homework Equations whats is the motion equation...

Homework Statement Use Maxwell's equations to derive the continuity equation. B=Magnetic Field E=Electric Field ρ=Charge Density J=Current Density Homework Equations Maxwell's Equations: ∇⋅E=ρ/ε0, ∇×E=-∂B/∂t ∇⋅B=0 ∇×B=ε0μ0(∂E/∂t)+μ0J Continuity Equation: ∇⋅J +∂ρ/∂t = 0 The Attempt at...

I made this excel file that is basically a calculator. It needs to create a Total price after fees, profit and supplier cost. Most profit margin calculators have you add a percentage for profit... this is not what I want. I have a hard dollar amount. You must know that the entire transaction...

A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...

Homework Statement Could someone explain how Legendre polynomials are derived, particularly first three ones? I was only given the table in the class, not steps to solving them...so I am curious. Homework Equations P0(x) = 1 P1(x) = x P2(x) = 1/2 (3x2 - 1) The Attempt at a Solution ...

I'm confused trying to understand the previous steps that lead to the formula for the angle of an ideally banked curve. In absence of friction, this is the angle where the Centripetal Force is provided by the horizontal component of the Normal Force. I understand that the Normal Force is...

I have been recently trying to derive the Einstein tensor and stress energy momentum tensor for a certain traversable wormhole metric. In my multiple attempts at doing so, I used a coordinate basis. My calculations were correct, but the units of some of the elements of the stress energy momentum...

I notice that the branch cuts for arcsin(z) are from -infinity to -1 and 1 to infinity. How do these choices for the branch cuts make the function single-valued? I am having trouble understanding the reasoning here even though these choices for the cuts are widely used/accepted.

Suppose I come up with a system that has certain number of particles with certain masses and are interconnected between each other in a certain way and are acted by forces which are also part of the system. What's the general rule for finding potential and kinetic energies as functions of...

I am given a formula in explicit form and as a recurrence relation. It is asked to derive the recurrence relation from the explicit form. How is this done?

Homework Statement Basically I wanted to see if anyone would be willing to give me the solution to the 4th problem of the Weinberg textbook on quantum field theory. The exact question in the book is "Derive the perturbation expansion (3.5.8) directly from the expansion (3.5.3) of old-fashioned...

The problem statement is: Assuming that we are in vacuum, and that the only work done between mechanical systems and electricity and magnetism comes from the Lorentz force, give a full, relativistic derivation of the Maxwell stress-energy tensor.

Homework Statement Using dimensional analysis deduce the relationship between the pressure drop per unit length along a cylindrical pipe of radius r, and the radius of the pipe, the viscosity of the fluid in the pipe, η, and the volume flow rate, V ̇ . Homework Equations Δp/l = 8ηV...

Homework Statement Derive Stefan-Boltzmann law from Wien’s law Hint: you can use (without proof) R(T) = -∞∫∞ R(λ,T)dλ , ρ(λ,T)=(4/c)*R(λ,T) Homework Equations wien's law: p(λ,T) = f(λ,T)/^5 Stefan's law : R(T) = σT^4 The Attempt at a Solution Honestly I am having trouble just...

Homework Statement Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive...

Phase difference between clocks with distance Homework Statement Derive Phase difference between clocks with distance Homework Equations I honestly don't understand how this equation ΔT = vD/c2 is derived/figured out. The Attempt at a Solution We haven't covered Lorentz...

Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise...

Here is the working leading up to this: The circuit is a series circuit, with Ro being the circuit's internal resistance and Rh being the heater's resistance. We're only concerned about the power transfer to Rh. We have an input with a constant voltage V. Ohm's law: V = IR, where R is the...

Edit: well this is frustrating, not sure why the itex things aren't working.. Edit2: I've attached a picture of the question at the bottom as well. Homework Statement The cohesive energy of a solid noble gas may be written as (See picture below) Derive an expression for the...

Homework Statement Derive: R=v^2sin2theta/g Show that R=V0^2/g Homework Equations The Attempt at a Solution This is my first time to take up physics so I have no idea at all on how to do this, to be honest.

Differentiation by first principles is as followed: $$y'=\lim_{h\rightarrow 0}\dfrac {f\left( x+h\right) -f\left( x\right) }{h}$$ So, assuming that ##y= e^{x},## can we prove, using first principle, that: $$\dfrac{dy}{dx}\left( e^{x}\right) =e^x$$ Or is there other methods that are...

Homework Statement Why can't you do integration-by-parts directly on the middle expression in equation 1.29--pull out the time derivative over onto x, note that \displaystyle \frac{\partial x}{\partial t} = 0, and conclude that \displaystyle \frac{d \langle x \rangle }{dt} = 0Homework Equations...

According to wikipedia, "The moving magnet and conductor problem", I stopped at the equation shown in the attachment. It said that the curl of the E` ( electric field in the frame of the conductor) is equal to minus of the dot product of the velocity of the conductor and the del multiplied by...

Given a sphere x^2 + y^2 + z^2 = a^2 how would I derive the surface area by using surface integrals? The method I've tried is as follows: dA = sec\ \gamma \ dxdy where gamma is the angle between the tangent plane at dA and the xy plane. sec \gamma = \frac{|\nabla \varphi|}{\partial \varphi...