Coefficients Definition and 753 Threads

Homework Statement Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) Homework Equations...

Homework Statement The 68 kg climber in Fig. 4-52 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.78 and 0.55, respectively. What is the minimum...

b_{n} = \frac{1}{\pi}\int^{\pi}_{-\pi}sin\theta sin n\theta d \theta let u = sin \theta, \ du = cos \theta d \theta dv = sin n \theta d \theta, \ v = -\frac{1}{n}cosn \theta = \left[-\frac{1}{n} sin \theta cos n \theta \right|^{\pi}_{-\pi} + \frac{1}{n} \int^{\pi}_{-\pi} cos...

Homework Statement If \sum^{n}_{r=0} \frac{1}{^{n}C_{r}} = a, then find the value of \sum^{n}_{r=0} \frac{r}{^{n}C_{r}} in terms of a and n.[/tex] The Attempt at a Solution I tried to write down the terms of both the series, but to no avail. i can't think of...

Homework Statement \sum^{n}_{r=0} (2r+1) (^{n} C_{r})^{2} The Attempt at a Solution x(1+x^{2})^{n} If I differentiate this and put x=1; I will get the above series without the squares of the binomial coefficients.Will multiplying by (1+x)^{n} help now?

Please provide me Diffusion coefficients of following ions in water at different temparatures (25 deg celcius, 75, 125, 300 etc) 1. Fe2+ 2. H2O 3. Fe(OH)+ 4. Fe(OH)2(aq) 5. H+ 6. OH- 7. CO3-2 8. H2CO3 9. HCO3- 10. Na+ 11. Cl-...

I was going through an inroductory book on PDE's and at one point they proceed with little show of work. I have problem with equation -yu_x + xu_y = u . Characteristics for this equation are x_t = -y, y_t = x, u_t = u . So far it is clear, but now books states that solution of first...

[b]1. Find Fourier Series Coefficient for a signal. (alternanate sawtooth pulse from t= -3 to 3 amplitude 1 on positivwe side and-1 on negative side. 3 pulse on positive side. 3 pulse on negative side. pulse width is 1.) as given in attachment file. [b]2. Compute the Fourier series...

polynomial equations whose coefficients are all matrices (was "I shouldnot") << post edited by berkeman to improve clarity >> That aside, I am looking for a free downloadable linear algebra book that will teach me about finding roots in polynomial equations whose coefficients are all...

AFAIK, there are two basic type of linear regression: y=ax+b and y=a2 + bx + c But I have to do the same with the function y = asin(x)+bcos(x). Here is what I have done: We have: \begin{array}{l} \frac{{\partial L}}{{\partial a}} = 0 \frac{{\partial L}}{{\partial b}} = 0Continue...

Homework Statement The odd periodic function f(x) is defined by f(x) = -4-x for -4 <= x <= 0 and 4-x for 0 <= x <= 4 f(x + 8) = f(x) Sketch f(x) for -12 <= x <= 8 Find the coefficients in the Fourier series for the function defined by equation (1) and write out the series...

Homework Statement f (x) = 0 -pi<x<0 x^2 0<x<pi Find the Fourier series and use it to show that (pi^2)/6=1+1/2^2+1/3^2+... Homework Equations N/A The Attempt at a Solution I was able to find the Fourier series and my answer matched with the back of the...

Hi, I was wondering if it is possible to express the norm of a function in terms of Fourier coefficient. If so, how do you go through it if given a particular function. Thanks

Homework Statement The function f(x) =ln(10 - x) is represented as a power series in the form f(x) = (sum from 0 to infinity) of c_{n}x^{n} Find the first few coefficients in the power series. The Attempt at a Solution I know how to find the coefficients in a normal looking...

Homework Statement A particle of spin 1 and a particle of spin 2 are at rest in a configuration such that the total spin is three and its z component = 1. If you measured the z component of the ang mom of the spin 2 particle, what values might you get and what probabilities for each...

Homework Statement Determine the relation that exists between the nth finite difference and the leading coefficient. Homework Equations ... I'm not too sure how to html it up properly, but the numbers/"n"s following the "a"s are meant to be sub-script: f(x) = anx^n + an-1x^n-1 + ... + a2x^2 +...

Hi, new here, I am looking for some help on this homework problem. pretty sure you need to separate yp into 2 parts? anyways, use method of undetermined coeff. to solve y" + y = x*cos(x) - cos(x) thanks.

[SOLVED] (Methods)Parameters v Undetermined Coefficients Can anyone tell me why I would use one technique over the other? It seems as though undetermined Coef. is much easier to do but I suppose that comes with limitations?

Homework Statement My textbook takes a look at the \Delta(1232) particle It says that \left|\pi p;\frac{3}{2},\frac{3}{2}\right>=\left|\pi;1,1\right>|N;\frac{1}{2},\frac{1}{2}\right> where N stands for a nucleon and pi could be any of the three flavours of pion. They then go on by applying...

Homework Statement In an L-R-C circuit, L = 1, R = 2, C = 0.25, E(t) = 50 cos(t) Find the steady state solution Homework Equations The Attempt at a Solution L \frac {di(t)}{dt} + R \frac {dq(t)}{dt} + \frac {q}{C} = 50cos(t) \frac {di(t)}{dt} + 2 \frac {dq(t)}{dt} + 4q...

Homework Statement Find the steady state solution: In an L-R-C circuit - L = 1, R = 2, C = 0.25, E(t) = 50cos(t) Homework Equations The Attempt at a Solution L \frac {di(t)}{dt} + R \frac {dq(t)}{dt} + \frac {q}{C} = 0 \frac {dq^2(t)}{dt^2} + 2 \frac {dq(t)}{dt} + \frac...

Hello, Here is my question: should the kinetic friction coefficient Fk be the same when the object with mass m is pulled with a constant velocity as the kinetic friction coefficient with the same mass m when it was pushed and released. The measurements in the second case were taken from the...

Homework Statement What should the coefficients a,b,c of the polinom P(x)=x^3+ax^2+bx+c be, so his roots x_1+x_2=x_3 ? Homework Equations P(x)=a_n(x-c_1)(x-c_2)...(x-c_n_-_1)(x-c_n) c_1+c_2+...+c_n= -\frac{a_n_-_1}{a_n} c_1c_2+c_2c_3+...+c_n_-_1c_n= \frac{a_n_-_2}{a_n}...

Hello. I'm designing a simple prototype home kit for visualising the effects of vibration on various systems. In this case i have a simple spring mass system in compression that will have responses measured by varying initial displacements. As it stands the system will be unforced, and...

Homework Statement Find an equation describing a body in free-fall in air. This is not really homework. I'm in a differential equations class write now, and I have fun finding real world applications for such things. Homework Equations m\frac{d^{2}y}{dt^{2}} = B\frac{dy}{dt}-mg The Attempt...

Hello there, I'm given the following population regression equation: PRICE(i) = β(0) + β(1)SQFT(i) + u(i) where the things in brackets are subscripts and SQFT represents the square footage. A sample of houses is then given with their cooresponding prices and square footage. I have solved...

Homework Statement 1. f is a function defined on the interval -a<x<a and has Fourier coefficients an=0 bn=1/n^(1/2) what can you say about the integral from -a to a of f^2(x)dx? 2. Show that as n goes to infinity the Fourier sine coefficients of the function f(x)=1/x -pi<x<pi tend to a...

Homework Statement Find solution for y'' + y' -2y = 2x with initial values of y(0) = 0, y'(0) = 1 Homework Equations I have found yc = c1*exp(-2x) + c2*exp(x), but finding yp is what I'm having trouble with... AND THEN I'm not so sure how to go about the initial value. The Attempt at...

Homework Statement tyʺ+yʹ=4t Homework Equations The Attempt at a Solution The problem that I am having with this problem is I've never been shown how to calculate the particular solution when there is an unknown (t) on the left hand side of the equation. If the problem were...

[SOLVED] Fourier coefficients Homework Statement For f \in C^{2\pi}\cap C^1[-\pi,\pi] , I have to show that \sum_{n\in\mathbb{Z}}|c_n(f)| < \infty where c_n(f) is the Fourier coefficient of f; c_n(f) = (f, e_n) = \frac{1}{2\pi}\int_{-\pi}^{\pi} f(t)e^{-int}\,dt f \in...

Greetings, Regarding the two procedures: undetermined coefficients and variation of parameters, can both procedures be used interchangeably - meaning they both solve (non-homogeneous linear equations)? Does one method work better in certain situations, if so which method is preferred when...

I'm trying to get my head around the idea of expansion coefficients when describing a wavefunction as \Psi(\textbf{r}, t) = \sum a_{n}(t)\psi_{n}(\textbf{r}) As I understand it, the expansion coefficients are the a_{n} s which include a time dependence and also dictate the probability of...

Can anyone tell me the coefficients of static friction for these material combinations? Or does anyone know where I might be able to find them. human skin - steel human skin - aluminum human skin - wood Thanks

I am looking for the form of a solution for a second order ODE with right hand side: x (sin x + 2) I'm thinking the form would be (Ax + B) sin(x) + (Cx + D) cos(x) + Ex + F. Does this seem correct? Thanks for any help or suggestions!

From J.J. Zakurai page no.222-225: We know that Clebsch-Gordan coefficients vanish unless m=m1+m2. Then, (1) why is that the terms in recursion relation doesn't vanish? since m1+m2=m+1 or m1+m2=m-1 in eqn.(3.7.49). (2) why is again in the example shown in eqn.(3.7.54), m1+m2=m? I...

Homework Statement The function f(x)=5xarctan(3x) is represented as a power series. Find the first few coefficients in the power series. Homework Equations The power series is represented in the form sum(Cn*x^n) The Attempt at a Solution I've attempted to write the function as an...

There are two functions f(t) and g(t); t is the independent variable. The distance between the two functions will be given by [1/2pi integral{f(t)-g(t)}^2 dt]^1/2 between -pi and +pi. Apparently, this distance also is the Fourier coefficient of each term in the Fourier expansion of a...

Are the coefficients of the CKM matrix the same for all interactions? If yes, why does the CP violation occur only in very specific interactions and not in all of then? If no, why does the coupling between family quarks interaction dependent? Thanks

I have a question about coefficients of capacitance.. Specifically I'm reviewing the treatment on the subject in Chap 3.6 in Purcell's classic book on E&M. He starts out by considering a system of four conductors (actually 3 main conductors, and an "infinte" boundary condition surrounding...

Homework Statement Homework Equations Using the Carnahan and Starling equation, estimate the coefficient of volumetric expansion, α, and the coefficient of compressibility, β, defined as α ≡ 1/V * (δV/δT) [holding P constant] and β ≡ -1/V * (δV/δP) [holding T constant] (I've used δ...

My understanding is that in GR the way in which the components of the metric tensor can vary from location to location in spacetime is determined or constrained by a number of factors: (1) the choice of coordinates (a mathematical constraint); (2) the distribution of mass/energy (a physical...

Hey! I was looking at some problems since I have a mid term tomorrow and don't get how to do this one perhaps someone can help! http://img143.imageshack.us/img143/3452/16856739ys6.jpg I don't know if I am doing this right but i went backwards and found the vector equation to look...

How do you read the table?

The question: How many grams of Ba(IO3)2 can be dissolved in 700mL of a 0.100M KIO3 solution at 25C? use activity coefficients for this. (Ksp of Ba(IO3)2 =1.57E-9) my answer: I used this equation: Ksp = (concentration) * (activity coefficient) well i found out that my ionic strength...

Hi, I'm having a bit of trouble with a problem here. The question is: Use the Method of undetermined coefficients to Find the general solution to th system: dx/dt = y + e^t dy/dt = -2x + 3y + 1 I've got the homogenous solution fine, however I'm having a bit of difficulty with the...

*note before reading: pretend that the superscripts are really subscripts, for some reason , Latex is making the subscripts into superscripts* I'm not sure if I'm interpreting the universal coefficient theorem for homology correctly. Let's say I have a Homology group H(X;Z). This is a...

Homework Statement Even at low density, real gases don't quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial expansion. Just working with the first order virial expansion we have: PV=nRT(1 + B(T)/(V/n)) B(T) is a virial coefficient. A...

Here is the problem: A hockey puck is hit on a frozen lake and starts moving with a speed of 13.0 m/s. Five seconds later, its speed is 5.20 m/s. (a) What is its average acceleration? I used the kinematic equation V=Vo+at to find the accerlation which came out to be -1.56 m/s^2...

hi, I've been searching around the site and found it pretty useful but I'm having a pretty tough time with a few questions i have its pretty much the same as This but the coefficient values are different, the problem I'm having is with the coefficients for the bends, could someone please...

A function f(t) can be represented by the expansion f(t) = \frac{1}{2}A_{0} + A_{1}cos(\omega t) + A_{2}cos(2 \omega t) + A_{3}cos(3 \omega t) + ... B_{1}sin(\omega t) + B_{2}sin(2 \omega t) + B_{3}sin(3 \omega t) + ... Do the constants A_{n} and B_{n} the same thing as the real and...