Coefficients Definition and 805 Threads

Homework Statement Find the first two non-zero terms in the Taylor expansion of \frac{x}{\sqrt{x^2-a^2}} where a is a real constantHomework Equations f(x)=f(x_0)+f^{\prime}(x_0)(x-x_0)+\frac{f^{\prime\prime}(x_0)}{2!}(x-x_0)^2+...+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n The Attempt at a Solution If...

let's say you are given the following matrix T: T11 T12 . . . T1n T21 T22 . . . T2n . . . . . . . ...

Hey, Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution. I've been trying...

Could someone provide me with a link or source which i can cite for the values of the hall coefficients of tungsten and silver. I have had no luck finding either of them that are proper sources. thanks

I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it...

Hi all, I've been fiddling around with this problem for a while. I intuitively understand that the parallel propagator is the path integral of the connection. I would like to be able to show the converse (connection is derivative of parallel propagator) mathematically, and I am having a...

Let $f:\mathbb R\to\mathbb R$ be a continuous function of period $2\pi.$ Prove that if $\displaystyle\int_0^{2\pi}f(x)\cos(nx)\,dx=0$ for $n=0,1,\ldots$ and $\displaystyle\int_0^{2\pi}f(x)\sin(nx)\,dx=0$ for $n=1,2,\ldots,$ then $f(x)=0$ for all $x\in\mathbb R.$ I know this has to do with the...

Is there a way to use the Clebsch Gordon coefficients tables to find the coefficients of a three particle system? For example if there is a system of three spin 1/2 particles, how to find the Clebsch Coefficients for different spin states using tables?(say for the state, |s12=0, S=1/2 ms=1/2>)

I'm curious about the validity of various techniques from good old calculus in one real variable when dealing with complex coefficients. I know enough complex analysis to know that the rules change when dealing with complex variables, but I'm curious about the case when the variables are still...

do you have a idea about it?can you help me http://img17.imageshack.us/img17/1156/18176658.png

Compute the sine coefficients for f(x)=e^{-x^{2}} on the interval [0,2\pi]. Does this mean f(x+2\pi k)=f(x), k\in\mathbb{Z}? Can x\in[0,\infty)?

Homework Statement Prove that \sum\limits_{k=o}^l {n \choose k}{m \choose l-k} = {n+m \choose l} Hint: Apply binomial theorem to (1+x)^n * (1+x)^m Homework Equations The Attempt at a Solution Using the hint, I started by saying that (1+x)^n * (1+x)^m = (1+x)^(n+m) =...

Homework Statement If; a*x + b*y = c*x + d*y x ≠ y a,b,c,d ≥ 0 Prove that; a=c b=d 2. The attempt at a solution I've been fiddling with this equation and have been getting nowhere.

Homework Statement I need to generate coefficients of hermite polynomials up to order k. Recursion will be used. Homework Equations a[n+1][k] = 2a[n][k-1] - 2na[n-1][k] The Attempt at a Solution Its not pretty, but here is my code. #include <iostream> #include <iomanip>...

Homework Statement I wanted to solve a ode which has Brownian motion as a variable coefficient Homework Equations 2x2y'' + y' -ρy = 0 where x is the Brownian motion with respect to time ρ is a constant The Attempt at a Solution I have tried power series with no solution. Is there a...

I am designing a test rig for golf clubs at the university of nottinghamm, and due to a large spending spree, don't have much of my budget left. As a result of which, I was hoping to use a door closer as a spring damper system. Does anyone have any idea of rough values of the damping...

The expressions for the coefficients of a Fourier series are valid for all integers [0;n]. Though sometimes when I evaluate the Fourier series of an even function (composed only of cosines) I get an expression for the r'th coefficient, which has r in the demoninator. It could be for instance...

Homework Statement Show that the generating function A(x) = \sum_n a_n x^n of a_n = \sum_{k=0}^n {n+k \choose 2k} 2^{n-k} satisfies A(x) = \frac{1-2x}{4x^2-5x+1}Homework Equations The Attempt at a Solution A hint was given to "interchange the sums". After doing that, I don't see how to...

1. Homework Statement x^3 +px^2 + 56x + q = 0 I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given. 2. Homework Equations Given that the three roots are all positive and...

Homework Statement x^3 +px^2 + 56x + q = 0I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given. Homework Equations Given that the three roots are all positive and are the first free...

Hi, I've got an equation stating p=a(r-1). If p represents prime number and r is a positive integer, and a is a constant, what can we conclude for the constant a? Like a $\in${-1, 1, -p, p}? I suspect this has something to do with modular arithmetic...:confused: Thanks.

The measured pH of 0.100 M HCl at 25°C is 1.092. From this information, calculate the activity coefficient of H+. I tried using the Debye-Huckel equation and got 0.825 but it's not right. I don't know how else to solve for the activity coefficient.

Homework Statement There is an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle θ = 20°. What is the magnitude of the acceleration of the block across the floor if (a)μs = 0.630 and μk = 0.540 and (b)μs = 0.400 and μk = 0.330...

The lifetime of the 32P1/2 to 32S1/2 transition of the Na atom at 5896 angstrom (one of the Na D lines) is measured to be 16.4 ns. What are the einstein a and b coeff? What is the transition moment in debye? What is the peak absorption cross section for the transition in angstrom2, assuming...

The connection \nabla is defined in terms of its action on tensor fields. For example, acting on a vector field Y with respect to another vector field X we get \nabla_X Y = X^\mu ({Y^\alpha}_{,\mu} + Y^\nu {\Gamma^\alpha}_{\mu\nu})e_\alpha = X^\mu {Y^\alpha}_{;\mu}e_\alpha and we call...

Hey all, there is something that has always bugged me in linear second order ODEs. We say that the general solution is: y=C_1e^{r_1x}+C_2e^{r_2x} where r_1 and r_2 are the solutions of the characteristic polynomial. The cases where r1, r2 are real are pretty straightforward. If they are...

Homework Statement I have two spin-1/2 particles and I need to calculate their Clebsch-Gordan coefficients.Homework Equations The Attempt at a Solution I followed the procedure of applying J_- to |{j,m}\rangle and J_{1-} and J_{2-} to |{m_1,m_2}\rangle and comparing them. I got correctly...

Do any of you know just a general range of friction coefficients for tires? I'm working out some braking problems, but can't really find anything searching online.

Homework Statement Given that p(x) is a polynomial defined by (x+1)(x^2+2)(x^4+4)(x^8+8)...(x^1024+1024) and knowing that the coefficient on x^2012 can be written as 2^a, find a. Homework Equations Binomial thereom mabye idk The Attempt at a Solution Tried grouping up terms that...

I'm told that factoring is an important skill in calculus so I am avoiding using the quadratic formula. But for quadratic equations with large coefficients to factor, is there a better/faster way rather than guessing and checking every single combination?

Hi, I am trying to solve the following equation: \Psi(r,t) = \sum_n C_n(t) e^{-i E_n t} \psi(r) to find the C_n(t)s. The system I am modeling is benzene. I can, by Hückel's method, determine the time-independent solution. The apparently obvious transition from time-independent...

Homework Statement For a given periodic function F(x), the coefficients An of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed: An =(\frac{2}{πn})sin(\frac{πan}{λ}) for n≥1 and...

Homework Statement For the differential equation y'' - 4y' + y = 0, (a) Show that if we let x = y' (i.e. x(t) = y'(t)), then this leads to the system: x' = 4x -y y' = x (b) Conversely, show that the system in (a) leads to y'' - 4y' + y = 0 (and x'' -4x' + x = 0 also). Homework...

Homework Statement Fidn the Fourier expansion for f of period 2Pi that corresponds to y=x/3 on the interval [0,2Pi) Im just a little confused about if I am setting up the integration properly. The asymmetric interval is kind of confusing me here. The Attempt at a Solution a0 = 1/Pi ∫ x/3 dx =...

Homework Statement Homework Equations Sum of roots taken one at a time is -b/a Sum of roots taken two at a time is c/a three at a time is -d/a four at a time is e/a The Attempt at a Solution I did part one by solving the two equations...

Thanks for any help! I'm trying to understand the coefficients of a 2d DFT. say we've got this matrix, f(a,b) \left( \begin{array}{ccc} 9 & 1 & 9 \\ 9 & 1 & 9 \\ 9 & 1 & 9 \end{array} \right) I used wolfram alpha's function, Fourier{f(a,b)} and the transform comes back as \left(...

If I wanted to solve this y''+3iy'+y=cos(2t) using undetermined coefficients. and I make the guess y=Ae^{2it} then i find y' and y'' and then solve for A. I get that A=-1/9 then I take the real part when I multiply it to Eulers formula. But when I plug this back into check it...

Homework Statement Show that the imaginary part of the solution of z''+z'+z=te^{it} is a solution of y''+y'+y=tsin{t} The Attempt at a Solution Ok so I first make the guess that z(t)=(at+b)e^{it} then I find z' and z'' and plug it back in and then equate the coefficients of t...

Awhile back A.T. & PeterDonis helped me through several basic confusions on my way to an intuitive understanding of geodesics in curved spacetime. I looked at http://www.relativitet.se/spacetime1.html http://www.adamtoons.de/physics/gravitation.swf...

Ok, so obviously, given some polynomial P(x) of degree r, it has r roots in the complex numbers by the FTOA, and if these roots are u_1, u_2,... it can be written as \begin{array}{l} P(x) = (x - {u_1})(x - {u_2})(x - {u_3}) \cdots \\ P(x) = {x^r} - ({u_1} + {u_2} + {u_3} + \ldots ){x^{r - 1}}...

Homework Statement I want to prove that coefficients of potential are non-negative. i.e. Pij ≥ 0 Homework Equations By coefficients of potential method we know that in a system of conductors the potential on ith conductor is related to charges on conductors by: \Phii = \sum Pij Qj...

I've been fooling around with the Fibonacci sequence for some time and I thought it would be interesting to see what would happen if I made the coefficients in a three variable system of equations follow that sequence. The results are intriguing and enigmatic. I discovered the following...

Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...

I'm working on a problem and I've run into a differential equation that very strongly resembles the biharmonic equation but is fundamentally different: 0 = a(∂^4 ψ/∂x^4) + b(∂^4 ψ/∂y^4) + c(∂^4 ψ/∂x^2 ∂y^2). where a,b,c are scalar coefficients. Any ideas? I think these were originally...

what will be the rate of acceleration be when a 10N force is applied to a 7.0kg block of wood resting on a table with a coefficient of friction equalling 0.45? ok so i am totally confused, I am thinking i have to use 2 formulas but I am not exactly sure i tried the formula: Fn = Fg = mg...

how would you find the rate of acceleration when given the force, mass, and the coefficient of friction?? what would the formula(s) be?? i am so confused! HELP!

Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0 If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the original ODE and then solve it analytically or is a numeric solution the only way?

Consider a flat 2-dimensional plane. This can be described by standard Cartesian coordinates (x,y). We establish a oblique set of axes labelled p and q. p coincides with x but q is at an angle θ to the x-axis. At any point A has unambiguous co-ordinates (x,y) in the Cartesian system. In...

The objective is to find some coefficients by comparing two equations. T_2 \cdot \frac{R_1}{R_1+R_2} + T_1 \cdot \frac{R_2}{R_1+R_2} and T_2 \cdot k_1 + T_1 \cdot k_2 I compare and set k_1 = \frac{R_1}{R_1+R_2} (1) k_2 = \frac{R_2}{R_1+R_2} (2) I expand the...

If f(x) has a period of 2*pi and |f(x)-f(y)| <= c*|x-y|^a where a and c are positive constants, why are are n-th Fourier coefficients <= c*(pi/n)^a ? Help or hints would be appreciated.