Coefficients Definition and 805 Threads

Hello everyone, my question isn't exactly a "Here's the data how do I do it" but rather why is it giving me "this" answer. I was doing a lab in class the other week, involving a pulley system which has one mass on a table and the other hanging. We had a balance to measure the masses and a...

Homework Statement http://edugen.wiley.com/edugen/courses/crs3098/rc/boyce3346c07/math/math1074.gif solve using the method of undetermined coefficients Homework Equations v(t)=a*t*e^-t + be^-t + ct + d The Attempt at a Solution what i could do is that i replaced v(t) for x in the...

Hello, I am looking at different ways to solve Systems of Linear Homogenous Differential equations with Constant Coefficients that is \acute{x}=Ax (x and x' are vectors A is a matix) then the solutions are x= \xi e^{\lambda t} where \xi are the eigenvectors and \lambda the eigenvalues of A and...

I want to know if there is a general solution to a second order homogeneous differential equation with variable coefficients?

Find the solution of: y" + 3y' = 72sin(3t) + 36cos(3t) where y(0) = 6 and y'(0) = 9 I first found the solution to the homogeneous eq: the roots (R^2 + 3R = 0) are R = 0, -3 which gives the family of solutions: y = a(1) + be^(-3t) and y' = -3be^(-3t) using the initial conditions...

Hello there, I have trouble understanding why the coefficients in an affine combination should add up to 1; From the wikipedia article (http://en.wikipedia.org/wiki/Affine_space#Informal_descriptions) it's mentioned that an affine space does not have an origin, so for an translation different...

Homework Statement y'' - 5y' = 2x^3 - 4x^2 -x + 6 The Attempt at a Solution I first found the m's on the left hand side. They are 0 and 5. I then found the m's on the right hand side. They are 0, 0, 0, and 0. I then wrote my interim equation: y = C1 + C2e^5x + Ax^4 + Bx^3 +...

Homework Statement y'' + y = sin x + x*cos x Homework Equations The Attempt at a Solution i don't like undetermined coefficients. so far, for me, it's been so much trial and error, although i am getting a little faster at it. anyway, i didn't work out the homogeneous equation...

Homework Statement Determine the constants c_{1},c_{2},c_{3},c_{4} of the column displacement equation where k=\sqrt{\frac{P}{EI}} In lab we subjected 3 specimens to a compressive load in a pinned-pinned and clamped clamped configurations. I have to compare theory results to...

Are coefficients of friction Ms and Mk independent of the weight being pulled? We just had a lab on friction and i am just curious about this. Thank you

Homework Statement A is an nxn square, real matrix. Let f(x) be the characteristic polynomial, write f(x) = xn - c1xn-1 + ... + (-1)rcrxn-r + ... + (-1)ncn Show that cn-1 = \sum det (Aii) where Aii is the (i,i) minor of A. Similarly, what is the coefficient cr? Homework Equations...

Homework Statement An oscillator is driven by a triangular periodic force (if that makes sense), which has period \tau = 2. (a) Find the long-term motion x(t), assuming the following parameters: natural period \tau[naught] = 2 (that is, \omega[naught] = π), damping parameter ß = 0.1, and...

Suppose n is even, prove: \sumk=0->n/2, C(n,2k)=2^(n-1)=\sumk=1->n/2, C(n,2k-1) Give a combinatorial argument to prove that: (I've figured out this one...) \sumk=1->n, C(n,k)^2=C(2n,n) For the first problem, I tried to break C(n, 2k) into C(n+1,2k)-C(n, 2k-1), but they didnt seem to work very...

Homework Statement what is the weight percent concentration of SO2 in the exsolved aqueous fluid phase that existed with solution if sulphur has ppm by weight of 90. partition coefficient= 47 Homework Equations partition coefficient- 47= concentration of aqueous fluid/ concentration of...

Homework Statement If a solid material is in the form of a block rather than a rod, its volume will grow larger when it is heated, and a coefficient of volume expansion beta defined by \beta = \frac{{{V_2} - {V_1}}}{{{V_1}\left( {{t_2} - {t_1}} \right)}} may be quoted. Here {V_1} and...

I have an equation of the form (1-x)(1-x^2)(1-x^3)\cdot\cdot\cdot(1-x^n). Or, in maple notation, product(1-x^a, a=1..n). I've been trying to find a way to express this as an expanded polynomial in sigma notation so that I can extract coefficients (for an enumerative generating function). If the...

Hi, I am trying to prove something, but I need some kind of a result on the coefficients of a power series. Suppose f(z) has a power series expansion about zero (converges). What can I say about the sum of the absolute values of the coefficients? Ideally I would like to show this sum is...

Homework Statement I have searched very long time. I need the kinetic coefficient of Polystyrene of Polystyrene, or even better Polystyrene on Glass. The polystyrene we are using is the stuff that is used to insulate hot water pipe. Homework Equations We do not know the weight of the...

Homework Statement I need to derive the following relation: \alpha_{S}=\alpha_{P}\frac{1}{1-\frac{\kappa_{T}}{\kappa_{S}}} Homework Equations Hopefully you can see that my notation |P means at constant pressure, I could not find a better way to do this, any ideas...

Homework Statement Not so much a homework problem, but a problem that is annoying me because of its simplicity. Not all cubic polynomials with rational coefficients can be factorized by the rational root theorem (or is this false?). What I am finding hard to comprehend is how a cubic with...

For a Sturm-Liouville problem, as in: \frac{d}{{dx}}\left[ {r(x)\frac{{dy}}{{dx}}} \right] + [\lambda p(x) + q(x)]y = 0 I've read in several books that one assumes that p, q and r are continuous, real-valued and bounded in the interval I, r' is continuous, and p>0. But I've never seen...

I have data for the radiation pattern of antenna, given as the theta and phi components of the electric field (E_theta, E_phi), with 0<theta<180 deg, 0<phi<360 deg. I want to describe this data as a spherical harmonic expansion. So, my task is to find the spherical harmonic expansion...

I've recently completed a fatigue lab for a CT specimen of steel, and I wanted to compare my computed values of Paris' Law coefficients with previously published data for error analysis. Does anyone know where I can find the values for C and m? Repeated Google searches have born me no fruit. It...

Homework Statement The motion of an undamped mass-spring system is described by the differential equation 2x" + 36x = sin(wt) a) For what values of w will the system exhibit resonance? b) Use the method of undertermined coefficients to find a particular solution in the case where w is not...

Hey guys, I've been reading up on binomial coefficients and I have found a brief section on n choose r. I understand vaguely what it actually is, however in my textbook there is a step by step proof of how we show that: ( \stackrel{n}{r} ) = \frac{n!}{r!(n-r)!} I can follow where...

Homework Statement Hi i would just like some fast hints, I'm doing the integrals wrong, I am splitting up the integral below and get the wrong answer. well it's about finding the Fourier series for f(t)={0 for -π<t<0 and sint for 0≤t≤π} Homework Equations a_{n} =...

When I was in college I found the abscissas and weights for a 32-point Gauss-Legendre Quadrature and wrote a program to do that. But I can't find that information now and need it again. It doesn't have to be 32-point; anything from 30 to 50 would be fine, but 16 digits of accuracy please.

given the infinite power series f(x)= \sum_{n=0}^{\infty}a_ {n}x^{n} if we know ALL the a(n) is there a straight formula to get the coefficients of the b(n) \frac{1}{f(x)}= \sum_{n=0}^{\infty}b_ {n}x^{n} for example from the chain rule for 1/x and f(x) could be obtain some...

We did a lab where we dropped three spheres into two different fluids, measured their velocities, and found drag coefficients. We were also asked some theory questions, and these are what I need help with. Spheres: 3.175 mm, 0.05 g Teflon 6.35 mm, 0.375 g, aluminum 12.7 mm, 8.36 g, steel...

been working on these all week some help please.. 9) 3y''-6y'+30y= 15sinx+exp(x)tan(3x) 10) y''-2y'+y= 4x^2 -3+ Exp(x)/x[b]2. Homework Equations Variations of parame Method of undetermined coefficients thoughts: i think that you need to split the eqtuaion into 2 parts. Using variation of...

Homework Statement Obtain the Taylor series solution up to and including order 3 of the following non linear ode y'=x^2+\sin y,y(0)=\frac{\pi}{2} Homework Equations After substituting the power series form of sin(y) I get: y'=x^2+(y-\frac{y^3}{3!}+\frac{y^5}{5!}-\frac{y^7}{7!}...)...

Homework Statement Determine the Fourier coefficients of the 3-periodic function and determine how many terms needed to keep 3 digit accuracy. f(t) = 1/2(1-Cos[Pi t]), for 0<t<1 f(t) = 1, for 1<t<2 f(t) = 1/2(1-Cos[Pi(t-3)]), for 2<t<3 Homework Equations For the cos...

This isn't really a question (other than to ask if this has been considered before) but rather an interesting observation. Lest anyone misunderstands the purpose of this post, I'm not trying to argue that maths is 'broken' or anything like that - maybe just that sometimes the 'obvious'...

Homework Statement y(4)-4y2=t2+et Determine the general solution Homework Equations The Attempt at a Solution So I worked it all out and got the correct answer. My question is that when we make the onsat that a particular solution will be in the form Y=At4+...how do we know it...

Homework Statement i have this problem y'' - y' - 2y= -6xe^{-x} Homework Equations this is the homogenous solution : y_{h}= c_{1} e^{-x} + c_{2} e^{2x} The Attempt at a Solution first i can do the problem but what is perplexing me is why of these two tentative...

Homework Statement After demonstrating that a set of functions are orthogonal and complete, Jackson presents equations like the ones shown below. I've used the equations for the Legendre series representation as an example, but he does almost the exact same thing with the Bessel functions...

Homework Statement A hollow right circular cylinder of radius b has its axis coincident with the z axis and its ends at z=0 and z=L. the potential on the end faces is zero, while the potential on the cylindrical surface is given as V(\varphi,z ). Using the appropriate separation of variables...

Homework Statement Hello, this is my first time posting, I've run into a bit of a snag in my physics lab. I am to figure out the coefficient of friction based on the values we found in the lab. Now I found them out however I just want to be sure that I am doing this right. these values were...

Use of "method of undetermined coefficients" Hi all, Suppose I have a equation f(z+1) - f(z) = z^{1/2} , \forall z \geq 0 eq (1) then is it possible to solve this equation by the method of undetermined coefficients ? It is usually seen in textbooks that the forcing function is taken to be...

Homework Statement So I'm supposed to show that a finite Fourier approximation is the optimal approximation for a given function. I am to suppose we have a given set of functions \phi _k(x),k=1,2,\text{...}N defined on a\leq x\leq b. They are orthogonal \int _a^b\phi _m(x)\phi _n(x)dx=0...

Homework Statement A sled is pulled at a constant speed over a horizontal surface where the kinetic coefficient of friction is .20. What is the minimum force necessary to keep the sled moving if its mass is 2 slugs? Homework Equations f(s)=U(s)N or f(s)=Ns(mg) F(s)= Frictional Force...

This is a question from a book in which I can't figure out, but it has no solutions at the back. Find the general solution to the PDE: xy ux + y2 (uy) - y u = y - x I've learned methods such as change of variables and characteristic curves, but I'm not sure how I can apply them in this...

Here is the problem i am having trouble: Expressing the binomial coefficients in terms of factorials and simplifying algebraically show that (n over r) = (n-2+1)/r (n over r-1) i got that equals ((n-r+1)/r) ((n!)/((r-1)!(n-(r-1))!)) but i am trying to get that to equal n!/r!(n-r)! which...

Homework Statement `Suppose it is known that the graph of the function y= ax^2 +bx^2+cx+d passes through four given points (x_i,y_i), i = 1,2,3,4. Write a user defined function that accepts these four points as input and computes the coefficients a,b,c and d. The function should solve four...

I have to determine the 18 connection coefficients \Gamma_{ij}^{k} for spherical coordinates. I know how to calculate said coefficients, but I'm not sure what all 18 are. Can anyone clarify what the possible combinations could be?

Homework Statement I have the following system og equations: \left\{\begin{array}{l} y + 2z = 1 \\ x + 4y + 3z = C \\ x + y + Bz = B \end{array}\right. a) Create the augmented matrix and reduce to row echelon form (I've already done this) b) For which values of A and B is...

Hi~ I'm having trouble with solving a certain differential equation. x2y'' + x y'+(k2x2-1)y = 0 I'm tasked to find a solution that satisfies the boundary conditions: y(0)=0 and y(1)=0 I have tried solving this using the characteristic equation, but i arrived at a solution that is...

I'm trying to find the activity coefficients of benzene and water in the liquid phase, they are in a solution of composition 20 and 80mol% which is beginning to form ice crystals. I know I need to use the 1 parameter margules activity coefficient model i.e. ln (gamma) = A x^2 and I have...

Can someone explain to to me how to find the general solution of the fourth order ODE y''''-y''=0 Right now I have y(x)=a+b*x+c*e^-x+d*e^x where a,b,c and d are constants. Not sure if this is correct just wanted to double check.

Homework Statement Find General Solution: y"+6y'+9y=e-3x-27x2 Homework Equations The Attempt at a Solution I know you have yh which is the general solution to the left side of the equation set to 0 and then fine the particular solution. When i try to find yp1 I get...