Coefficients Definition and 753 Threads

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...

Can anyone help me to get the general solution of the linear partial differential equations with variable coefficients of any order?

Homework Statement Problem #4 from here: http://www.math.washington.edu/~jtittelf/ExtraCredit.pdf Homework Equations ? The Attempt at a Solution There's only one example of using undetermined coefficients in my textbook. I'm not sure where to start. x = t2a + tb + c ? That's...

Homework Statement Derive a formula of the form \int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b) that is exact for polynomials of the highest degree possible. Apply a change of variable: y=x-a Homework Equations The Attempt at a Solution I don't get the "highest...

http://img243.imageshack.us/img243/156/55139700.png Knowns Well I know that \sum \frac{1}{1-x} = 1+x^{2}+x^{3}... I know the integral is [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP32919a6dgiib73geda500000hd72bah4i062h1b?MSPStoreType=image/gif&s=36&w=241&h=38 I've...

I'll make this post short. The problem just asks me to something in the form x'=Ax (A is a 2x2 of constants) and then describe the behavior of the solution as t approaches infinity. My solution is x=C1e-2t(2/3 1)T + C2e-t(1 1)T. Since both vectors are multiplied by 1/et, my solution...

Homework Statement Given are the points (1,-4), (3,0), and (4,1). I am to usemethod of undetermined coefficients. Homework Equations Given these points I am to find a quadratic equation. The Attempt at a Solution Sorry! But I really do not have any clue. May anyone help me?

I understand permutations, combinations and such, but I can't seem to make sense of binomial coefficients, or at least the notation. As an example, could someone walk me through the notation for a generic problem.. something like 100 people eligible for an award and the winner can choose 1...

Homework Statement Find the unique solution to the differential equation y''+4y'−5y=−435sin(2t) satisfying the initial conditions y(0)=29 and y'(0)=47 The Attempt at a Solution So (I think) I found the correct general solution. I let y(t)=Acos(2t)+Bsin(2t) and eventually worked...

Homework Statement Find the Clebsch Gordon coefficients of 1/2 \otimes 1 = 3/2 \oplus 1/2 Homework Equations We have some properties of the CG coefficients which might be useful: 1) they are nonzero only if j is between j1-j2 and j1+j2 2) m = m1+m2 for nonzero coefficients 3)...

Hello mathematicians, I'm creating a program and I need in this program to rotate some planes around the origin, while I'm given the coefficients a,b,c and d for this plane, they represent a plane of the form: a x + b y + c z = d So these coefficients are given and I want to rotate the...

Homework Statement y''-49y=7cos(7x)+7+e^(7x) The Attempt at a Solution I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one. First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...

I am working on a section on undetermined coefficients of a difference. I'm really trying to understand the material, but am struggling. y_{n+1}-2y_{n}=2 I got as far as saying for the homogenous equation y=c_{1}(-1)^{n}. I'm assuming the guess next would be A, but I'm confused. Maybe if...

Homework Statement y''-4y=60e4t y(0)=9 and y'(0)=2 Homework Equations none in particular The Attempt at a Solution First I solved for the auxiliary equation. r2-4r r(r-4) r=0, 4 So the general solution for the homogenous form is C1e0x+C2e4x where C1 and C2 are unknown coefficients to...

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...

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...

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 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!}...)...

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...