Approximation Definition and 768 Threads

I recently read a paper titled : " The Saros cycle: obtaining eclipse periodicity from Newton's laws " My question is, more or less: " Is it possible to obtain an approximation of G by observing Saros periodicity ? " I'm currently studying the derivations of the Lunar , Solar, and Stellar...

I have a problem with static/non-static spacetime. The problem is that the notion of spacetime includes time itself, so how can it change with time? Imagine an asteroid approaching the Earth-Moon system. The Earth-Moon system is a non-static spacetime, so presumably is giving off gravitational...

Homework Statement Hello, I have a question about using Eulers Method to approximate a solution to a differential equation. The problem lists forces that would be applied on an object and influences its velocity and therefore its position. I believe I am doing the Euler method correct to...

Hi! I read from Perry Green's ChE Handbook that the friction factor for Re ≤ 2,100 can be approximated by ƒ = 16/Re. But there was this question that I encountered (though I don't know the source) and according to it, ƒ = 64/Re for laminar flow. Can someone clarify which is which? Thank you!

Homework Statement y'+y=3+x y(0)=1 (a) Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h = 0.1. Homework Equations yn+1 = yn + f(x0, y0)(x-x0). Adjusting 0 for the next number as we go up The Attempt at a...

My apologies for having to post in an image, my latex skills are not good enough for the question at hand :( a) There is no solution since the system has more unknowns than equations (the equations are equal giving 1=2 which does not make sense). b) I get a solution of \begin{bmatrix}1 \\1 \\...

According to rules for working with approximate data, why the final result of a multiplication or division involving approximation data is round off so that the result has as many significant digits as the given data with the fewest significant digits? How is this rule established? For example...

Dear forum people in the Slater-Koster approximation interatomic matrix elements is a function of the cosine direction. How to calculate cosine direction for silicene by sp2 hybrid.

Dear forum people in the Slater-Koster approximation interatomic matrix elements is a function of the cosine direction. How to calculate cosine direction for silicene by sp2 hybrid.

The authors of a physics textbook want to determine the number of grains, N in a beach of 500 m long, 100 m wide, and 3 m deep. They assumed that each grain is 1-mm-diameter sphere. They also assumed that the grains are so tightly packed that the volume of the space between the grains is...

Homework Statement I put up the image so that you can see the hints if you're curious. I am supposed to prove that if ## S=\sum_{n=0}^{\infty}a_{n}x^{n}## converges for ##|x|<1##, and if ##|a_{n+1}|<|a_{n}|## for ##n>N##, then $$|S-\sum_{n=0}^{N}a_{n}x^{n}|<|a_{N+1}x^{N+1}|\div (1-|x|)$$...

Say that we have a continuous, differentiable function f(x) and we have found the best approximation (in the sense of the infinity norm) of f from some set of functions forming a finite dimensional vector space (say, polynomials of degree less than n or trigonometric polynomials of degree less...

Homework Statement Prove: Hint: Group the terms in the error as ##(a_{n+1}+a_{n+2})+(a_{n+3}+a_{n+4})+\cdots## to show that the error has the same sign as ##a_{n+1}##. Then group them as ##a_{n+1}+(a_{n+2}+a_{n+3})+(a_{n+4}+a_{n+5})+\cdots## to show that the error has magnitude less than...

Hello, I just recently found out that one could find the Friedman's equation in Newton's approximation (without GR) by assuming that the universe in homogeneous and isotropic simply by using F=ma and the conservation of energy. On can then find that the scale factor goes as t^2/3, as expected...

Homework Statement A monochromatic light source is used with a double slit to create an interference pattern on a screen that is 2.00 meters away. If the 2nd bright spot is observed 8.73 mm above the central maximum, can the small angle approximation be used? Show and/or explain your reasoning...

What is the physical interpretation of the Weisskopf-Wigner approximation, when it is applied in the neutral kaon system? I would say that the approximation means that a decay state has a small probability to suffer a transition (or be "transformed") into another decay state through weak...

Regarding interacting green's function, I found two different description: 1. usually in QFT: <\Omega|T\{ABC\}|\Omega>=\lim\limits_{T \to \infty(1-i\epsilon)}\frac{<0|T\{A_IB_I U(-T,T)\}|0>}{<0|T\{U(-T,T)\}|0>} 2. usually in quantum many body systems...

Hello! (Wave) Approximating $y'(t^n)$ at the relation $y'(t^n)=f(t^n,y(t^n))$ with the difference quotient $\left[\frac{y(t^{n+1})-y(t^n)}{h} \right]$ we get to the Euler method. Approximating the same derivative with the quotient $\left[\frac{y(t^{n})-y(t^{n-1})}{h} \right]$ we get to the...

Hello All, Light travels at 1,86,000 m/sec. i.e.2,99,338 km. The distance from Earth to Moon is 3,84,400 km. Is there any constellation or any physical object (to have an idea) which is not near to moon but falls within the range of 2,99,000 km? Just for curiosity. Thanks

Homework Statement The question is : Calculate the work done in joules when 1.0 mole of N2H4 decomposed against a pressure of 1.0 atm at 300 K for the equation: 3N2H4 (l)→4NH3(g)+2N2(g) Homework Equations None The Attempt at a Solution I did it like as: Assuming 100% dissociation of N2H4 4/3...

I am trying to determine the optimum length of the control vectors for a cubic Bézier approximation of a $90^\circ$ circular arc. However to my limited mathematical mind the equation cannot be solved algebraically. Wolfram Alpha even finds it too complicated. However I am told that it IS...

Homework Statement To rephrase the question, given a power series representation for a function, like ex , and its MacLaurin Series, when I expand the two there's no difference between the two, but my question is: Is this true for all functions? Or does the Radius of Convergence have to do with...

What is the physical meaning of this approximation? Qualitatively I'm finding it hard to know what differentiates it from other approximation methods...

http://www.mth.uct.ac.za/omei/gr/chap7/node3.html Shouldn't eq 45 have a minus sign, looking at eq 29. Although I'm confused because the positive sign makes sense when comparing with the Newton-Poisson equation. I can't see a sign error in eq 29. (I believe the metric signature here is...

The weak field approximation in the Newtonian limit shows that the coordinate acceleration along a geodesic is related to the gravitational force. The geodesic deviation equation relates the coordinate acceleration between adjacent geodesics to tidal forces. If I drop 2 balls together from the...

Hi all, I'd like to ask about " the vacuum saturation approximation " in a calculation as the decay width of ## B \to l \nu ## [hep-ph/0306037v2] equ. 1 till equ. 4, that why ## < 0 | \bar{u} \gamma_\mu b | B > ~ and ~ < 0 | \bar{u} b | B > = 0 ## ? and for ## [ \bar{l} \gamma^\mu...

Homework Statement ##\frac{\partial u}{\partial \phi}=-\frac{Me}{J^{2}}sin\phi + \frac{M^{3}}{J^{4}}(-\frac{1}{e}sin\phi+e^{2}sin2\phi+3e\phi cos \phi )##. Assume this to be ##0## at ##\phi=\pi+\epsilon##. Find ##\epsilon##? Homework Equations The only method I can think of is to expand out...

I have a second order differential equation of the form (theta is a function of time): \theta ''=F\left(\theta ,\theta '\right) Turning them to two first order equations I get: \begin{cases} \theta '\:=\omega \\ \omega '=F\left(\theta ,\omega \right) \end{cases} And here's the algorithm...

Hey guys, So I have a question about the gauge invariance of the weak field approximation. So if I write the approximation as \Box h^{\mu\nu} -\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha})+\partial^{\mu}\partial^{\nu}h=0 then this is invariant under the gauge...

Hey! So we're deriving something in Daniel Schroeder's Introduction to Thermal Physics and it starts with this: \Omega \left( N,q\right) =\dfrac {\left( N-1+q\right) !} {q!\left( N-1\right) !} Both N and q are large numbers and q >> N. The derivation is in the book, but I am always...

Homework Statement I have a pretty simple question. I was going over an older exam when I encountered something that did not quite make sense to me. If \frac{(2s+5)(-s+0.5)}{(s+3)(s^2+0.1s+0.01)}, find a low order approximation for the system. I understand that the pole at s=-3 can be...

Hi, I am working on TDR (Time Domain Reflectometry). I send a 7GHz bandwidth fast rising edge (14ns) square wave into a coax. I get a return Signal. I have an ADC with 10Msamples/sec. I am using MPLAB IDE for coding the microcontroller. Now I would like to increase the Points on the...

Hi I am new member and I am new to the Signal processing so I hope I could get some help from the members to able to understand the concepts. I have a Signal. I have a 10Msaples/sec ADC. I view the Signal on an Oscilloscope which has 20Gsamples/sec sampling rate. The Point where I am...

Homework Statement I'm trying to understand an approximation Griffiths does (in his solutions' manual - exercise 9.18-b) and I'm not quite getting it. Let $$k = \omega \sqrt{\dfrac{\epsilon \mu}{2}} [\sqrt{ 1 + (\dfrac{\sigma}{\epsilon \omega}})^2-1]^{1/2}$$ He says that, because ##\sigma >>...

So, I ve been trying to add orientation to my model of the flight dynamics of a rocket but I ve been running into a lot of problems. I didn't bother actually doing the math for the moments of inertia and everything because I guess it really doesn't have that much of an effect on the general...

Homework Statement please check attachment Homework Equations please check attachment The Attempt at a Solution since the deviation from f_0 to f is linear then we can write f=f_0 + C where C is some constant this should be enough to prove the first question (i think so) for the second...

< Mentor Note -- The OP's question was in the thread title. They have been advised to please make more detailed and clear thread starters > thanks

if , then what will be . In fact I was solving the integral equation by the method of successive approximation.

Homework Statement With unity position feedbck, i.e. make K2=0, plot root locus as a function of pitch gain (K1). By imposing 2nd order system approximation, estimate settling time, rise time, peak time of the closed-loop system with 20% overshoot. Pic of system...

how does this aproximation reduse the integral

A one dimensional potential field V(x), and its solution of SE, is divided into three regions. And the solution has two coefficients in each of these regions. There are six boundary conditions: two on each of the boundaries, plus two global boundary conditions. Now, as I wish to refine the...

How is the Born-Oppenheimer approximation used in Molecular Dynamics simulations? And in which situations does it break down?

Homework Statement Find the limit of: ##\frac { \Gamma (n+\frac { 3 }{ 2 } ) }{ \sqrt { n } \Gamma (n+1) } ## as ##n\rightarrow \infty ##. Homework Equations ##\Gamma (p+1)=p^{ p }e^{ -p }\sqrt { 2\pi p } ## The Attempt at a Solution Mathematica and wolfram Alpha gave the limit as 1. My...

Dear friends, let us use the definition of Lebesgue integral on ##X,\mu(X)<\infty## as the limit ##\int_X fd\mu:=\lim_{n\to\infty}\int_Xf_nd\mu=\lim_{n\to\infty}\sum_{k=1}^\infty y_{n,k}\mu(A_{n,k})## where ##\{f_n\}## is a sequence of simple, i.e. taking countably many values ##y_{n,k}## for...

Homework Statement The stirling approximation, J! = √JJ+1/2e-J, is very handy when dealing with numbers larger than about 100. consider the following ratio: the number of ways N particles can be evenly divided between two halves of a room to the number of ways they can be divided with 60% on...

Chebyshev polynomials and Legendre polynomials are both orthogonal polynomials for determining the least square approximation of a function. Aren't they supposed to give the same result for a given function? I tried mathematica but the I didn't get the same answer :( Is this precision problem or...

In the Drude model of the free electron gas to explain the conduction of a metal, the relaxation time approximation that the electron has a collision in an infinitesimal time interval ##dt##is ##dt/\tau##. It can be shown that the mean time between collisions is ##tau##. If we choose an...

Homework Statement w!/(w-n)! = number of ways of distributing n* distinguishable particles in w distinguishable states w = number of distinguishable states n = number of indistinguishable particles How many ways are there to put 2 particles in 100 boxes, with no particles sharing a box...

Homework Statement Hello guys, I fail to understand a mathematical approximation I see in a solved exercise. The guy reached a partition function of ##Z=\sum_{l=0}^\infty (2l+1) \exp \left [ -l(l+1) \frac{\omicron}{T} \right ]## and he wants to analyze the case ##T>> \omicron##. He states...

First, I already know that when we have to do linear approximation of ##f(x, y)## if ##\Delta z = f_{x}(a, b)\Delta x + f_{y}(a, b)\Delta y + \epsilon_{1}\Delta x + \epsilon_{2}\Delta y ##. and ##\epsilon_{1}## and ##\epsilon_{2}## approaches to nought wneh ##(\Delta x, \Delta y)## approaches...