Coefficients Definition and 753 Threads

hi, if i have a cylindrical rod of copper and i heat is at one end face while the other surface areas are open to the atmosphere then besides the conductivity of copper i will also need the convective heat transfer coefficient to analyse the setup. my question is : how do can we estimate...

For any characteristic polynomial determined from A - eI (where A is a nxn matrix, e is an eigenvalue and I is the identity matrix), is it a rule that the coefficient associated with the char. polynomail term of highest degree must be positive ? My tutor made a theory that if the...

Homework Statement I've been having problems with a number of these things, here's the first one: y'' -2y' -3y = -3te-t Homework Equations I know that the general solution will be y = yh + yp where yh is the general solution to the homogeneous equation, and yp is the particular...

Homework Statement Find a particular solution. 1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution) 2. y'' + 16 y = 3 sin (4t) Homework Equations The Attempt at a Solution 1. I guess...

Hi, If we change coefficients in Homology, we can use the universal coefficient theorem to find the change in the homology group. Still, is there a way of knowing what happens to _individual classes_ under this change of coefficients? I am just thinking of cases where there is a...

Homework Statement where a=lowering operator, ad=raising operator ad^(2)+a*ad+ad*a+a^(2) just need to find the coefficients Homework Equations ad|n>=sqrt(n+1)|n+1> a|n>=sqrt(n)|n-1> The Attempt at a Solution ad^(2)=?|n+2> ad*a=n|n> a*ad=n|n> a^(2)=?|n-2> just reviewing and can't get...

I'm struggling in an application of Fourier transform.here is my problem: a series of points from experimental data plotted as a cruve. I'm planning to do a Fourier transform to see how smooth the curve is? my question is: is it possible/useful to calculate the Fourier coefficients? if yes, how...

Hey guys, I'm working on a MATLAB program to find Fourier coefficients. The problem with it: it gives a graph that has a different period and amplitude than the original function (although its the same general shape). I've uploaded a screenshot of the graph that I'm referring to (as an...

I want to write an algorithm that gives as output the numbers a_n,\ldots, a_1,a_0, when a matrix A\in\mathbb{R}^{n\times n} is given as input, such that \det (A - \lambda) = a_n\lambda^n + \cdots + a_1\lambda + a_0,\quad\quad\forall\lambda\in\mathbb{C} If n=2, a_2 = 1,\quad a_1 =...

I found a claim in a paper (BSSA, Vol 81, No. 6: "A Waveform Correlation Method for Identifying Quarry Explosions", By D.B. Harris) concerning finding filter coefficients. The statement is given without proof. I cannot locate a reference or theorem for the following, and have not been able thus...

Today I read about the AKS - Primality test in which the simple theorem For gcd(a, n) = 1, we have (X - a)^n\equiv X^n - a\ (mod\ n)if and only if n is prime. was proven. The if direction is quite trivial from the fact that \binom{p}{k}\equiv 0\ (mod\ p) for 1\leq k < p. The other direction...

Hello all, I am new to the ODE solvers in Matlab and am trying to learn: First, I am solving a 2nd order ODE to determine x(t), x'(t), and x''(t). No problem. Then, I am using these solutions to calculate two coefficients (that are functions of time) that are used in a second, second order...

Hi, I've come across a problem in my differential equations book that I can't seem to be able to solve (it's not a homework problem, I'm just practicing): "Using matrix algebra techniques and the method of undetermined coefficients, find a general solution for x''(t) + y'(t) - x(t) +...

Hi, All: The intersection form ( , ): H_n(M,R)xH_n(M,R)-->Z ; Z the integers and R any coefficient ring, in a 2n-manifold is well-defined in homology, i.e., if (x,y)= c , and x~x' and y~y' , then (x',y')=c Still, how is the value of the intersection form affected by changes in...

Ok, please view the attached image for the Question, and for the given solution. I need some help understanding the solution. I can get the Complimentary equation with no problems, I understand how to do that. However, some questions 1) Why do we first ignore the sin(3x) in our...

Homework Statement Suppose we are given the following information about a continuous-time periodic signal with period 3 and Fourier coefficients a_{k} 1. a_{k} = a_{k+2} 2. a_{k} = a_{-k} 3. \int_{-0.5}^{0.5}x(t)dt = 1 4. \int_{0.5}^{1.5}x(t)dt = 2 Determine x(t) Homework Equations if x(t)...

Anybody know where I can find data on normal street-tire friction coefficients on dry asphalt? I'd like both the static, and the kinetic coefficients. If not, can somebody give me a range of reasonable values? While I'm at it... What about racing slicks on asphalt? I found one source...

Homework Statement suppose that we have the continuous time signal x(t) = cos(4πt) with fundamental period of T=1/2Homework Equations a_{k} = \frac{1}{T} \int_{T}{}x(t)e^{-j\omega_{0}kt}dt where \omega_{0} is obviously \frac{2\pi}{1/2} = 4\pi well the problem is that this integration...

hi , can anybody give me some examples of 'systems of linear differential equations with periodic coefficients'? i don't know how to solve it.. where can i get problems and solutions on this?

Hi all, I came across a linear recurrence with polynomial coefficients and realized that I don't have a clue as to how to solve it. The usual methods like generating functions or guessing seem not to work in that case. Here is the equation: i (i - 1) (i - 2) b[i] = 1/3 (i + 1) i (1 -...

Homework Statement Calculate the following sum: (click to expand)The Attempt at a Solution I tried something with Moivre formula and Newton binomial theorem but no result :redface:, should i continue with these or is there any simpler approach? I just need some hints. Thanks.

Can anybody tell me how to calculate Clebsch-Gordon coefficients? I see a table given for the coefficients in some books (Griffiths p200), but it is not clear how to read the table. Any help would be appreciated.

Homework Statement I need to sum the binomial coefficients that are divisible by a positive integer t, i.e. \sum_{i=0}^{s}\binom{ts}{ti} Is there any way to get rid of the sum sign? Homework Equations Let t be fixed and s go to (positive) infinity (both t and s are positive...

I have a set of data points (x0, y0), (x1, y1), ... (xi, yi) With each yi there is an associated error ei. The data is modeled by the function: y = a\exp(-bln^2(c/x)) I have determined values for the coefficients a, b, c and I know the residuals produced from the values of the...

Homework Statement the problem is to solve this differential equation: x^2 y'' + xy' + (4x^2 - 1)y = 0

Hi guys, I need the dynamic friction coefficient between steel and teflon. Do you know where I can get it? Thanks

[PLAIN]http://www.undeclaredcomics.com/wp-content/uploads/2011/06/rsz_2011-06-06-everyone-gets-it-except-you.png

Homework Statement Decide whether or not the method of indetermined coefficients can be applied to find a particular solution of the given equation: The attempt at a solution I think the answer is yes, because the equation is of the form: a\ddot{y}+b\dot{y}+cy=F(t)where F(t) is the...

Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...

Homework Statement Find the solution of the given initial value problem. \[y''-2y'-3y=3te^{2t}\]Homework Equations The Attempt at a Solution(1) the homogenous solution is given by \[y_{h}=c_{1}e^{3t}+c_{2}e^{-t}\] (2) the particular solution is in the form \[y_{p}=(At+B)e^{2t}\] (3) The...

for a system defined as y(n) + a1y(n-1) + a2y(n-2) = bx(n), for what values of a1, a2, and b is the system realizable? i know that the transfer function is obtained by the following H(z) = Y(z)/X(z) H(z) = b/(1 + a1z-1 + a2z-2) H(z) = bz2/(z2 + a1z + a2) i also know that the poles have...

Homework Statement An electron with kinetic energy 5 eV (8.01E-19 J) passes through a 3 eV (4.806E-19 J) potential barrier. There are certain widths for this potential barrier in which the transmission probability will equal one hundred percent and the reflection probability will equal zero...

Homework Statement y" + y = 2/sin(x) solve for y Homework Equations I tried to use variation of parameters to solve this but I don't know how to check it. The Attempt at a Solution y = -2xcosx + (constant)cosx + 2ln(sin(x))sinx + (constant)sinx How do I do this using...

Hi there. I had some trouble trying to solve this: y''+y=\cos x +3\sin 2x (1) At first I just found the solution for the homogeneous equation: y_h=e^{\lambda x} \rightarrow \lambda^2+1=0 \rightarrow \lambda_1,\lambda_2=\pm i Then y_h=C_1\cos x+ C_2 \sin x So I've tried to find the particular...

Homework Statement Hi. I have this problem, which says: The equation x^2y''+pxy'+qy=0 (p and q constants) is called Euler equation. Demonstrate that the change of variable u=\ln (x) transforms the equation to one at constant coefficients. I haven't done much. I just normalized the equation...

Homework Statement The function f(x)=ln(10-x) is represented as a power series: \sum^{\infty}_{n=0}a_{n}x^{n} Find the first few coefficients in the power series. Hint: First find the power series for the derivative of . The Attempt at a Solution Okay, start seems fairly...

Does the variable coeffcient in linear differential equations have to be polynomials? All the examples I have found seem to be polynomials for example the Cauchy–Euler equation. For example is sin(x)y'' + cos(x^2)y' + y = 0 still considered a linear differential equation with variable...

Homework Statement Calculate [x^n] (1-2x+x^2)^{(-k)} Homework Equations Just the geometric series.The Attempt at a Solution This is what I got so far [x^n] (1-2x+x^2)^{(-k)} = [x^n]((x-1)^2)^{(-k)} = [x^n] \frac{1}{(x-1)^{(2k)}} Basically, how do I put this into a sum form? or can I just...

Hi, everyone: If we change the coefficients used to calculate homology, the universal coefficient theorem tells us how the homology changes. Still, is there a way of knowing whether a specific (non-trivial) cycle under certain coefficient is still a cycle after the coefficient...

Homework Statement y-(sinx)2)dx + sinx)dy Homework Equations Since the result wouldn't be a line, the equation would only be linear in one of its variables. The Attempt at a Solution y-(sinx)2 = 0 ; sinx = 0 --- y = (sinx)2 + sinx No clue... Also, is there more than one way to...

Homework Statement The following is the output of a 16 point computation of the discrete Fourier Transform for data taken at 10 kHz. Complete the table below by determining the frequencies associated with each of the FFT values. I attached an Excel workbook with the table. Homework...

Hi. I'm trying to make a simple model of a condensation based countercurrent heat exchanger where liquid water and steam flows are separated by a conducting wall. I formed the equations as Q = \frac{T_{steam}-T_{water}}{\frac{1}{Ah_{water}}\frac{d}{Ak_{wall}}\frac{1}{Ah_{steam}}} = L\dot{m}...

have been solving PDEs by sep of variables, and the solution that comes out is generally a summation the general look of it is something like: U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t The above may not be exactly right, I was thinking along the lines of heat equation where...

Hi all! I'm trying to solve the following system of ODE's, but somewhat unsuccessful... \dot \vec x = [-i\omega(t)\sigma_z - \nu(t)\sigma_y]\vec x with sigma_i the Pauli matrices and w(t) and v(t) well-behaved functions of t (actually I also have that w = 1+v). Nevertheless, v(t+T) =...

y''-2y'-3y=-3te^-t i know that that the general solution to this problem is yh = c1e^3t + c2e^-t i am having trouble figuring out what the particular solution is (yp) i keep getting the yp = 3/4te^-t , but wolfram alpha is telling me that the answer is something else. how do i get...

Homework Statement Prove that a polynomial f of degree n with coefficients in a field F has at most n roots in F. Homework Equations The Attempt at a Solution So we could prove this by induction by using a is a root of f if and only if x-a divides f. My question is: why do...

Hi everyone I'm modeling the dynamics of a cantilever that has a non-constant linear density profile, i.e. \rho(x)=\rho_{1} \0 \leq x \leq x_{0} \rho(x)=\rho_{2} \0 x_{0} \leq x \leq l \rho(x)=0 \0 otherwise My differential equation is: \frac{ d^4 \phi(x) } {d x^4} = \phi(x)...

I'm working on undetermined coefficients for nonhomogeneous equations. I have an equation that is equal to 3xe^x. For an earlier one that was equal to e raised to 8x, I used Ae^8x; but on this one, obviously that won't work. I don't know what I should be looking at. I tried Axe^x but no dice...

http://www.cs.odu.edu/~toida/nerzic/content/problem_solving/problem_solving.html example 3 ========================================= Quote Problem: Given that a, b, and c are odd integers, prove that equation ax2 + bx + c = 0 can not have a rational root. Understanding the Problem: This is a...

Homework Statement Find the Clebsch-Gordan coefficients associated with the addition of two angular momenta j_1 = 1 and j_2 = \frac{1}{2} Homework Equations The table of coefficients. The Attempt at a Solution I think I am misunderstanding something important here. I can't see...