Approximation Definition and 705 Threads

The equation is attached in the image file. I tried several times to work it out but I can't figure this out for the life of me. They just want me to show that the first equation equals the second one. Any atmospheric/meteorology majors out there? Any help in general would be appreciated.

I need to know how to find the normal approximation of B for cast iron from the B-H curve. I know for sheet steel, I can use a B of 1 and get 400 for H and use B=μH to get 0.0025 Wb/At-m. How is it done for cast iron?

hi, I have 2 localized states in a hydrogenic atom.. we're in dipole approimation. I have to proof that <b| [p,V] | a> = <b| grad(V) |a> or equally: <b| V grad |a> = 0 (this is the dipole approximation in acceleration form) someone can help me? you can see...

I'm learning to deal with h2+ (hydrogen ion) problems and the like, which sure entails the infamous born oppenheimer approximation . i know the word "adiabatic" in a thermal sense, that is , an adiabatic process is the one in which no heat transfer occurs between the things of question and...

Homework Statement "Use a fixed-point iteration method to find an approximation to \sqrt[3]{25}that is accurate to within10^-4" i need the solution in step by step ... Homework Equations x=g(x) The Attempt at a Solution all i can get is the range \sqrt[3]{8} \leq \sqrt[3]{25} \leq...

Homework Statement I'm so confused about the derivation of the famous equation v=\sqrt{\frac{T}{u}}, I tried to derive it by myself but failed, then I turned to wikipedia but the derivation there really gave me a shock! http://en.wikipedia.org/wiki/Vibrating_string" I have no idea...

Homework Statement I was following a derivation of some laws and I didn't get how they approximate some portion of the expression. That portion/part is exp[gbH/(2kT)]. The book says gbH/2 <<1 and therefore exp[gbH/(2kT)] = 1+gbH/(2kT). Homework Equations The Attempt at a Solution I agree with...

Two very narrow slits are spaced 1.8 \mum apart and are placed 35.0 cm from the screen. What is the distance from the first and second dark lines of the interference pattern when the slits are illuminated with coherent light with \lambda =550 nm r1-r2=m\lambda dsin\theta=m\lambda...

I'm trying to do an integral, in which the integrand is composed of arbitrary functions and contains a derivative of the variable of integration. Further still, the integral is over a discontinuity. Because these are arbitrary functions I assume there is no exact solution, but I'm looking for...

Homework Statement I've found in a physics book that when u <<L, we have \sqrt {u^2+L^2} -L = \frac{u^2}{2L}. I don't understand why.Homework Equations Not sure.The Attempt at a Solution I've calculated the Taylor expansion of order 2 of \sqrt {u^2+L^2} -L but I couldn't show the...

Hello again! Facing some problems (my exam is taking place tomorrow... help is needed. Many thanks in advance!) I need to find an approximation for a retarded time. I don't understand how. This is what my lecturer wrote: sin(\varphi-\omega t)=exp(i\varphi'-i\omega(t-r/c)-i\omega(r'cos\theta...

[b]1. Homework Statement [/ Using the approximation, explain why the second derivative test works approximation=f(x0+delta x, y0+delta y) delta x and delta y are small... Homework Equations f(x0+delta x,y0+delta y) The Attempt at a Solution ok so i know the first derivative...

Hi Is there anyone here who has a good understanding of using approximation theory and parameter estimation techniques who can help me understand a chapter of a paper, and why certain techniques have been used. I have tried to use the given data, and matlabs optimization tools to follow the...

Hi, in the derivation of the Born-Oppenheimer-Approximation you have the Hamiltonoperator H=T_n + H_e, where T_n is the kinetic energy of the nuclei and H_e the electronic Hamiltonian. The Schroedinger equation to solve is: H \Psi = E \Psi Now, what people do, is the following ansatz: \Psi =...

Hi, everybody Let n_1 ~ Poisson ( \lambda_1 ) and n_2 ~ Poisson (\lambda_2). Now define n=n_1-n_2 . We know n has "Skellam distribution" with mean \lambda_1-\lambda_2 and variance \lambda_1+\lambda_2, which is not easy to deal with. I want to find the Pr(n \geq 0) . Is it...

Something has been bothering me for quite some time and when you cannot figure it out yourself ask a higher power, which happens to be this forum. Basically, at low energies we use the Newtonian definition of kinetic energy which is Ek = 1/2MV2 Now at high energies/high volecities it turns into...

Homework Statement estimate the ground energy of a bound qqbar system , the total hamiltonian can be written as , H(r)=2m-a/r+br+p^2/m,where a=0.5, b=0.18Gev^2, m being the mass of quark or antiquark the book kinds of gives Hint " p may be approximated as 1 over r" ,natural unit is...

Homework Statement Use the differential to estimate the volume of tin a can of radius 4 cm., height 12 cm. and thickness 0.04 cm is made of.Homework Equations (differential) df = f'(x,y)dx + f'(x,y)dy The approximated volume should be 14cm^3. However, I need the procedure to get to the...

Homework Statement Model the vibrating quartz-crystal thickness monitor as a mass(m)-spring combination, where k is the spring constant. a) What is the resonant frequency? b) Show that as additional mass \delta m deposits the the difference in resonant frequency or frequency shift is given...

This is not a homework question I'm just trying to understand quantum mechanics. I have found a Hamiltonian that has the potential engery part it as [eFr cos(wt)]. All of the variables are known but I can't identify what F is. It just states that F denotes the amplitude of the external field...

1. Find the first four nonzero terms of the power series approximation of the solution. y"-4y = 4t-8e-2t y(0)=1, y'(0)=-1 2. y=\suma_n*t^n where the summation goes from 0 to infinity 3. I have done a homogeneous problem similar to this and had no problems finding the first four...

In the Schutz book, "A First Course in General Relativity" (bottom of p.42 if you have it), it states the following: For small v, the energy is: E = po = m(1-v2)-(1/2) =(approx) m + (1/2)mv2 I can't figure out why this is! For small v, the LHS will tend to m, and the RHS will tend to m, so...

It is basically an integration that cannot be properly solved, so I look for an approximation or maximum&minimum bounds of f1(m) and f2(m) such that f1(m) < f(m) < f2(m). Here is the integral: f(m) = Integrate [ exp( -0.5* (sin(x)^2) *m) dx, x=0:pi/2] where m is a variable. When I take sinx ~...

Homework Statement In the beta decay of tritium (1 proton, 2 neutron) to helium, the emitted electron has a kinetic energy of 19keV. We will consider the effects on the motion of the the atomic electron (the one orbiting the nucles) which we assume is initially in the ground state of...

"Differential Approximation" A person of height 1.9m is walking away from a lamp-post at 1m/s. The light on the lamp-post is 5.1m above the ground. 1. At what rate (in m/s to the nearest cm/s) is the length of the person's shadow changing? 2. At what speed (in m/s to the nearest cm/s)...

Homework Statement Let f(x) = cos(pi*x), 0 < x < 1. Find a quartic approximation to f(x): By solving the continuous least squares problem using Chebyshev polynomials. By solving the continuous least squares problem using Legendre polynomials.Homework Equations The Attempt at a Solution For...

Homework Statement I have this equation: T=(1+\frac{U_{0}^{2}}{4E(U_{0}-E)}sinh^{2}(2 \alpha L))^{-1} Where α is given by: \alpha = \sqrt{ \frac{2m(U_{0}-E)}{\hbar^{2}}} I have to show that in the limit αL>>1 my equation is approximately given by...

Homework Statement storage of heat, T at time, t (measured in days) at a depth x (measured in metres) T(x,t)=T0 + T1 e^{-\lambda} x sin (wt - \lambdax) where w = 2pi/365 and \lambda is a positive constant show that \deltaT/\deltat = k \delta^2 T / \deltax^2Derive the second order Taylor...

Pls. answer in the simplest and the most intuitive way. 1. What is the reason our quantum field theory needs perturbative approach. Is it because in the concept of fields, there is an infinite number of freedom in the oscillations of the virtual particles, or is it because the field is...

Electric Dipole and Electric Potential.. and binomial approximation! Homework Statement An electric dipole at the origin consists of two charges +q and -q spaced distance s apart along the y-axis. a.)Find an expression for the potential V(x,y) at an arbitrary point in the xy-plane...

Homework Statement A player located 18.1 ft from a basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle Θ = 34 degrees and initial velocity of v = 25 ft/s.A. Show that the distance s of the shot changes by approximately 0.255∆Θ ft if the...

When we study something with our physics theory, we may always ignore some "unimportant" factors to simplify the culculation.And then, we get a approximation. But if we don't ingore any factors, we will get the absolutely accurate result. Is it possible? I think the physics theory isn't...

Homework Statement I trying to figure this out, its part of a bigger question. When ka \ll 1, what happens to, \frac{1}{\left ( 2-k^{2}a^{2} \right )\textup{sin}\, ka\, - 2\, ka \textup{cos}\, ka} Homework Equations Its something to do with the lowest order approximation. The...

"The Probing of, Approximation to and Idealization of Structure" for Foundations Hey, Over the past six years I have worked with Lucien Hardy at Perimeter in Waterloo and Prakash Panangaden at McGill. This paper is the culmination of thoughts on physics gleaned from that work...

"Random Phase Approximation" (Why they call it so?) Hi, I'm wondering that why the scientists call this phenomena in many body physics "Random Phase Approximation". (Why Random? Why Phase?) It seems that when we want calculate a correlation function in quantum field theory, it leads to...

Im trying to calculate the ground state energy of Helium using a density functional theory approach combined with the local density approximation. So far I have set up universal functionals and I mainly need help with the actual algorithm the evaluation of the Hartree energy functional.

Homework Statement find the 2nd, 3rd, and 6th degree taylor approximation of: f(x) = 10(x/2 -0.25)5 + (x-0.5)3 + 9(x-0.75)2-8(x-0.25)-1 for h = 0.1 to h = 1, with \Deltah = 0.05 and where xo=0; and x = h Homework Equations N.A The Attempt at a Solution I just need to...

Prove \hbar\omega << k_{B}T \Rightarrow \frac{\hbar\omega}{e^{\frac{\hbar\omega}{k_{B}T} - 1}.

In A First Course in General Relativity, the use of the weak field approximation is confusing to me. I constantly get confused when the term "f(x) is only valid to first order in f..." for the Newtonian potential in the metric comes up. At a certain point the book states: ...1/2(-1/(1 +...

Hi I'm trying to figure out how to get the electric dipole selection rules for an atom with many electrons. In all textbooks that I've seen it's shown for Hydrogen, or in the central field approximation (which is, in some sense, equivalent to Hydrogen). Obviously the central field...

Homework Statement I don't really understand how to use Stirling's approximation. here's an example you flip 1000 coins, whts the probability of getting exactly 500 head and 500tailsHomework Equations N!=NNe-N(2pieN)1/2The Attempt at a Solution wht they did was 21000 total number outcome...

y' = 3 + t - y, y(0) = 1 A) Find the approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, 0.4 using the Euler method with h = 0.1. B) Repeat part A with h = 0.05. Compare the results found in A. I did part A correctly, but cannot get the right...

Homework Statement Here is a drawing with all the needed variables: http://i.imgur.com/192GI.jpgHomework Equations The Attempt at a Solution I have been trying to figure out how this approximation is derived for some time now and have no progress to show for it. Any help in figuring out the...

Homework Statement Suppose a set of N data points {(xk,yk)}Nk=1 appears to satisfy the relationship for some constants a and b. Find the least squares approximations for a and b. Homework Equations The Attempt at a Solution I really have no idea about this problem.

Homework Statement Let f: R-->R be continuous. For δ>0, define g: R-->R by: g(x) = (1/2δ) ∫ (from x-δ to x+δ) f Show: a) g is continuously differentiable b) If f is uniformly continuous, then, for every ε>0, there exists a δ1>0 such that sup{∣f(x) - g(x)∣; x∈R} < ε for 0<δ≤δ1The Attempt at...

1. The problem statement, all variables and givennown data 1)FInd the nth left endpoint approximation Ln for f(x) = 3x^2-2 on [0,2]. What is the limit as n approaches infinity Ln in this case? 2)Evaluate: \sum45i=5 (2i-5) Homework Equations Ln = \sumNj=1 f(cj)(xj-xj-1) The...

Hi Homework Statement I'm trying to follow and work through a derivation in my textbook, making sure I can replicate the steps myself and understand what's happening. However, I came across this approximation and can't seem to figure out where it comes from or why and the book gives no...

Hi, Where can I find the expression of the central difference approximation of the first and second derrivative (spatial) for a NON uniform grid?

Can someone explain the attached image for me please? I do not understand how 2\delta_{k, k'}a_{k'}^{\dagger}a_{k} becomes a_{k}^{\dagger}a_{k} + a_{-k}^{\dagger}a_{-k} to me it should just be 2a_{k}^{\dagger}a_{k} and also I do not understand how e^{-ik}a_{-k}a_{k} +...

I am reading the H. A. Bethe's book ---quantum mechanics of one and two electron atoms. In section 39, it is shown how to go from general form to pauli approximation form through momentum space. who knows how to go directly in position space?