Coefficients Definition and 753 Threads

Homework Statement Set up but do not solve for the appropriate particular solution yp for the differential equation y''+25y=2xsin(5x) using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x). Homework Equations The Attempt at a Solution I first solved the...

I am trying to find the Fourier coefficients for the following signal: For some reason, I keep getting 0, which doesn't make sense to me. I am even getting 0 for F0 even though there is clearly area under the curve. Here's my work for this part: Period = T/2 Natural freq = 4pi/T F0 =...

Let V be the space of polynomials of degree 3 or less over \Re. For every \lambda\in\Re the evaluation at \lambda is the map ev_{\lambda} such that V \rightarrow \Re is linear. How do we find the coefficients of ev_{2} in the basis dual to \{1,x,x^2,x^3\}?

The eigenvalue problem of Schroedinger equation can be solved in a variety of ways. The continued fraction method can be stated by the following recipe: - represent the solution of the D.E. as a power series - replace back this solution into the D.E. - obtain a three term recurrence relation...

Right so basically, I'm doing a multicomponent distillation with some exotic chemicals. My feed comes in at 13kPa and 60*C, so it's under vaccum. This will be a two phase mixture. What I need is the vapour-liquid-equilibrium coefficients, 'K- values' at feed conditions. I'm basing this on an...

Homework Statement Solve the quadratic equation z^2 + 4(1 + i(3^0.5))z - 16 = 0 Homework Equations The Attempt at a Solution I think I've done this correctly, I just wanted to verify. I've only done the solution for k=0...

Homework Statement Find the solution of the system x' = 3x + 4y; y' = -2x-3y satisfying x(0) = 2 and y(0) = -1 Thank you Homework Equations The Attempt at a Solution My method involves linear algebra: turn the pair of equations into a single first order vector differential equation of...

Homework Statement Find the solution of the equation v''- 4v'+5v=0,such that v=-1 and v'=1 when x=pi=3.14159Homework Equations ... The Attempt at a Solution I treat it as a polynomial=>r^2+4r+5=0 =>delta=-4=>r1=2+2i and r2=2-2i v=e^[x+2](A*cos[2]+B*i*sin[2]) v=-1=e^[pi+2](A*cos[2]+B*i*sin[2])...

I'm kind of stuck in my search, hoped to be able to find some answers on this board. Anyways, I've been taksed to design a slow speed mixer and I'm trying to look up information beyond Stokes Law of FD = 6 pi r V u The fluid to be mixed is approx. 100000 poise, incompressible fluid. I'm...

x y'' + (x + 1) y' = 2 x Solve for y(x). Due to the coefficients being a function of x, I have no idea where to start to find the homogenous solution (Complementary Function). I know how to proceed after this part with the variation of parameters method. I just have no idea where to...

Homework Statement Find and prove a formula for sum{ (m1 choose r)(m2 choose s)(m3 choose t) } where the sum is over all nonnegative integers r, s, ant t with fixed sum r + s + t = n. Homework Equations The Attempt at a Solution I first attempted to find the number of combinations of r...

Hi Few months ago, I had written to PUMA, ADIDAS, NIKE etc. for the shoes with high coefficients of static friction, so that I can make more informed decision when I go to these shops next time. None of them replied. I know that, these big companies do a lot of research on the shoes. They...

Homework Statement Prove that for an integer n greater than or equal to 2, nC1 - 2nC2 + 3nC3 - + ... = 0. (nCm means n choose m) Also, 2x1 nC2 + 3x2 nC3 + 4x3 nC4 +... = n(n-1)2^(n-2) Homework Equations (1+t)^a = 1 + aC1(t) + aC2(t^2) + ... The Attempt at a Solution I don't know...

If we have a vector that can be expressed in terms of some finite list of basis elements. If we have an orthonormal basis for a vector space V, then a vector v can be expressed as <v,e1>e1 +...+ <v,en>en. This appears to be widely used for many results (such as Gram-Schmidt), but the...

Homework Statement For t\in\mathbb{R}, let: A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right] Get the solution for the general equation: X'=A(t)X Homework Equations The Attempt at a Solution I done many of these problems, all with constant...

How to calculate 1) binomial coefficients and 2) binomial distribution on a Casio fx-9860G calculator?

Hello! How do I prove ? Thank you! (it can be proven by using the convergence of the Fourier series in L_p-norm, but I want to use the above result to prove the convergence in L_2-norm, so I want to avoid that)

Correct me if I'm wrong. :) I'm starting to learn basics of the ordinary differential equations, and I have some troubles understanding the concept and method as a whole. I understand when to use the method of undetermined coefficients (MUC) as opposed from variation of parameters. Suppose...

I have a three term recurrence relation \[ a_0=1, \] \[ a_1=p_1(1)a_0, \] \begin{equation}\label{recurr} \begin{array}{ccc} a_{n}=p_1(n) a_{n-1}+p_2(n) a_{n-2}, && n\ge2.\\ \end{array} \end{equation} where \[...

Homework Statement You are given that the roots of the auxiliary equation associated with the linear, differential equation \phi(D)y = 2x- 3xe^{-3x} are m = \pm2,0,0. Write down the form of a particular solution of the differential equation as predicted by the method of undetermined...

I have the problem "Find the particular solution of 4y''+4y'+y=3xex. What would be the assumed function y? Like would it be Ax ex?

y''+9y=sin(3t) I need to solve the above using the method of undetermined coefficients. I have already found the solution to y''+9y=0 is c1(Cos3t)+c2(sin3t). The problem is finding the particular solution. From class I am aware that the general form of the solution is...

Undetermined Coefficients, just a piece i need help with please In one of the last steps in trying to find the Coefficients of Yp (particular solution), I am supposed to set coefficients of similar terms equal to each other. Here's where i need help: i have A(e^x) + (-2B-2C+2F+E)sinx +...

Hello, I know how to get the full Fourier series with complex coefficients and with real coefficients, and I know the relationship between An, Bn and Cn. However, I don't know why the relationship between them is what is it. Can someone either explain to me where the relationship comes from...

Homework Statement Your family just had anew refrigerator delivered. The delivery man has left and you realize that the refrigerator is not quite in the right position, so you plan to move it several centimeters. If the refrigerator has a mass of 180 kg, the coefficient of kinetic friction...

letsa say i have an ak = cos ( k*Pi/4) + sin(3*k*Pi/4), the signal is discrete time, fundamental period N=12. the way i would derive its x[n] is.. Sum(k=0, to 11 of: 0.5*exp(j*k*Pi/4) *exp(j*k*w*n) + 0.5*exp(-j*k*Pi/4) *exp(j*k*w*n) + (1/2*j)*exp(j*k*3*Pi/4) *exp(j*k*w*n) -...

I know how to do Frobenius on variable coefficient ODE's but only when the coefficients are powers of the independent variable. Can I do method of Frobenius on something like: y'' + e-xy = 0 ? What form would I assume a solution of? Just the regular y=sum(Akxk+r ? Thanks for the help!

Homework Statement Find a particular solution of y'' + 2y' + 5y = e^x * sin(x)Homework Equations The Attempt at a Solution Characteristic equation: r^2 + 2r + 5 = 0. Through quadratic formula, r1 = -1+2i and r2 = -1-2i, so my homogeneous equation is y_h = c1 * e^(-x) cos(2x) + c2 * e^(-x) *...

Homework Statement y''+y'=g(x) fundamental set of solns. of the homog. DE is: y1= 1 , y2= e^-x If g(x) = x^2 , yp1 = ____ Homework Equations The Attempt at a Solution I actually am looking at a key to an old test my teacher gave as a review for a test. The key has the...

first off I'd like say thanks to everyone on here, I've lurked and solved many questions thanks to you guys. First post woo. Basically we were tasked to design and carryout a lab to measure the coefficients of friction between a wooden board and some random objects (teachers gone for a few...

Hi, I'm doing a question using the Fresnel power coefficients, not the Fresnel amplitude coefficients. We can use MATLAB for this, but we are given a fixed angle of incidence of 45 deg so its really just one calculation, as opposed to an earlier question where the angle varied between 0 and...

I have been researching on the net and books for some time now. I have a few tables and equations but was wondering if anyone has the one I am looking for? I'm looking for a table that lists Wavelength(nm), Extinction Coefficient(k), Absorption Coefficeint(a) and Density(d) values from ~300nm...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

Homework Statement Solve using Method of Undetermined Coefficients: y'' - 2y' + 3y = 15t - 8 The Attempt at a Solution First I used the characteristic equation to solve for the homogeneous solution to get: yh = C1e-t + C2e3t Great. Now I need to find the particular. I am...

Homework Statement Find the Fourier series coefficients X_k of the periodic signal: x(t) = 5cos(6w_0t+pi/2) (digital or discrete spectrum) Homework Equations The Attempt at a Solution I am really confused with all of this and don't...

Homework Statement find a polynomial P(x) which has nonnegative coefficients. If P(1)=1 and P(5)= 426, then wast is p(3) Homework Equations P(1)= 6 P(5)= 426 P(3)= xThe Attempt at a Solution I have tried to use guess and check. I can't find a way to solve algebraically.

I am writing a paper publishing scientific data. My background is chemistry but I have taken a couple of stat classes. In my opinion, one of the biggest deficiencies in modern research publications is the improper use of statistics. I hope to avoid making this mistake, but I need your help...

Homework Statement y''' + y'' - 6y' = 36x Homework Equations y'' + y' - 6y =18x^2 The Attempt at a Solution I've integrated the third order D.E. to get a second order D.E. Solving the characteristic equation, to find a general solution, I get: y = c_1exp(-3x) + c_2exp(2x)...

Homework Statement y'' + 3y' + 2y = 24exp(-2x) Homework Equations y'' + 3y' + 2y = 24exp(-2x) The Attempt at a Solution I've solved the characteristic equation and am after the particular solution. I've let y_p = Aexp(-2x), y_p' = -2Axexp(-2x) and y_p'' = 4Axexp(-2x) When...

Hey I am designing a pipe system for a class and am required to calculate headloss. At one point in the design, a pipe splits into 4 smaller pipes and then these rejoin to recreate a pipe at the original pipe. I can't seem to find the loss coefficients associated with the quadfurcation and...

I have a conceptual problem regarding the following scenario: Try to imagine a triangle with two blocks on each side, attached together with a rope, and a pulley at the tip of the triangle. Block A & B are attached to each other through a rope. Blocks A & B are in static equilibrium, each on...

Homework Statement Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy |an| <= K/n and |bn| <= L/n n=1,2,... Homework Equations an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx Sorry if my form is slightly...

Homework Statement A rope exerts a force of magnitude of 21 N, at an angle 31 degrees above the horizontal, on a box at rest on a horizontal floor. The coefficients of friction between the box and the floor are s=0.55 and k=0.50 . The box remains at rest. Determine the smallest possible mass...

Homework Statement Given the first cycle of a waveform: f(t)=2u(t)-2u(t-1)+u(t-2)-u(t-3) -- Plot the first cycle of the wave form -- Find the Fourier Coefficients Homework Equations Given above The Attempt at a Solution No idea yet. Will appreciate any help.

Here is a paper written by me: http://www.voofie.com/content/84/solving-linear-non-homogeneous-ordinary-differential-equation-with-variable-coefficients-with-operat/" Basically, it uses operator method to solve linear non-homogeneous ordinary differential equation with variable...

Homework Statement A certain metal whose thermal expansion coefficient \beta is 5,0 × 10^-5 °C^-1 and whose isothermal compressibility \kappa_T is 1,2 × 10^-6 atm^-1 is at an initial pressure of 1 atm and an initial temperature of 20°C. A thick layer of Invar is thermally insulating the...

Trying to self-teach myself more quantum mechanics. Reading Zare's "Angular Momentum- Understanding Spatial Aspects in Chemistry and Physics". I don't really understand how to calculate eigenvalues of J using CG coefficients (I mean, I know the eigenvalues of J, just trying to calculate them a...

Homework Statement Find integers a,b, and c such that m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1) for all m. Then sum the series 1^3+2^3+3^3+...+n^3 Homework Equations I think I need to use m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1) and...

Hey folks! I am studying from a thermodynamics text (engineering thermo) and I am a little confused with the wording in the following development of the "Equation of Reaction Equilibrium": I am a little confused as to the distinction between the n's and the v's. Is it saying that the n's are...