Coefficients Definition and 805 Threads

Homework Statement For an even function, the Fourier series takes the form ^{\infty}_{n=0}\Sigma A_n cos(\frac{2\pi n x}{\lambda}) where \lambda is the wavelength of the function. In this problem you will see how to find the Fourier coefficients A_n. a.) Prove that A_0 =...

Hello, I'm trying to find a table of basic connection coefficients. My GREAT desire is to find a table that includes the metric, connection coeffs, Riemann tensor, Ricci tensor and Ricci scalar for NORDSTROM's 1913 scalar theory of gravity. Does anyone know an online source of this info...

Hi all, I was reading Lasers and i read something like this: for spontaneous emission, the rate of decay of electrons in high-energy state to low energy state is given by: \frac{dN_2}{dt} = P_{21}N_2 where P21 is equal to the probability of electron to drop from higher energy state...

I'm having some problems recognizing duplication when using the undetermined coefficients method to solve homogeneous type differential equations. http://college.cengage.com/mathematics/larson/calculus_early/3e/shared/chapter15/clc7eap1504.pdf Example 2 on Page 1119, could someone explain...

Homework Statement [PLAIN]http://pokit.org/get/d9a4a8542c2acdfedbb1038292f6817b.jpg Find the coefficients of this function Ck Homework Equations The Attempt at a Solution \begin{align}\Large C_{k}=\frac{1}{T}\cdot \int_{-T/2}^{T/2} f(t)\cdot e^{\frac{-jk2\pi t}{T}}dt=\frac{1}{T}\cdot...

Homework Statement The function f(x)=ln(2−x) is represented as a power series in the form: \sum C_{n}x^{n},n,0,inf Find the first five coefficients in the power series. Basically, this is a problem from my online homework. I did a lot of work to get to my answers, and I feel sort of tired to...

A single-phase ac voltage regulator has a resistive load of R= 10 ohms, and the input voltage is Vs = 240 V, 50 Hz. The delay angle of each of the Thyristors is ɑ = Π/2. Determine: (a) The rms value of the output voltage. (b) The Fourier coefficients of the fundamental, 11th and 13th current...

y''(t) - \frac{2}{t^2}y(t) = 3 - \frac{1}{t^2} In this problem I had to solve two ways: Variation of Parameters and Undetermined Coefficients. I solved it using Variation of Parameters and got the correct answer for the particular solution in the back of the book being y_p(t) = t^2ln|t| +...

hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks

I'm given: y''-y'+\frac{y}{4}=3+e^{\frac{x}{2}} and asked to solve it using undetermined coefficients. Using the auxilary equation y=e^{\lambda t} I got y_{1}=e^{\frac{x}{2}}, y_{1}=xe^{\frac{x}{2}} Now to solve the particular solution, I chose to guess: y_{p}=axe^{\frac{x}{2}}+b and...

Homework Statement This isn't really homework, just research I'm doing for myself... we start by defining: \sin_\ell(x) = (1 - \frac{1}{1+\tan^\ell(x)})^{\frac{1}{\ell}}\,\,\,for\, \,\,x \in [0, \pi] for \ell divisible by two, or \frac{1}{\ell} divisible by two. \sin_\ell(x + \pi) =...

Homework Statement For flat spacetime the coefficients of the Lorentz transformation are defined as \alpha^{\nu}_{\mu} = \frac{\partial x^{' \nu}}{\partial x^{\mu}} Whereas the Lorentz transformation is \begin{pmatrix} x_1' \\ x_2' \\ x_3' \\ x_4' \end{pmatrix} = \begin{pmatrix}...

Hello all: I'm using a code for solving partial differential equations that describe transient advection and diffusion. I'm more of a chemistry person, so I'm a bit lost on some of the basics of the calculation method. A general question: As my calculation progresses, I see that...

Homework Statement Hello. I need help with orthogonality of the Fourier series coefficients. I know you can use the dirac delta function, (or the kronecker function) in the orthogonality relationship. I want to try and see the derivation using complex form rather than sines and cosines...

Hello, I'm trying to find the coefficients for the ideal gas specific heat at constant pressure in the form: Cp = a + bT + cT^2 + dT^3 (kJ/kmol.K) I need to find these coefficients for Octane. I have found them online in a slightly different form.. Cp = a + bT + cT^2 + dT^3 + eT^4...

Homework Statement x(t)^double prime-x(t)=tsint Homework Equations The Attempt at a Solution in this case would I start this as x=t(A(2)+A(1))sint or do i also have to use the cos which makes it x=t(A(2)+A(1))sint+t(B(2)+B(1))cost?

Homework Statement determine the particular solution for the differential equation 2x^double prime+x=3t^2 Homework Equations The Attempt at a Solution since F(t)=3t^2 I used At^2+Bt+C and the first derivative is 2A+B plugging back in I get At^2+(4A+B)t+(2B+C)=3t^2 is this...

Homework Statement Find a particular solution y_c to the complex differential equation y'' + 2 y' + 3 y = -1 exp(2 i t) y_c= Using the solution y_c, construct a particular solution y_{1p} to the following differential equation y'' + 2 y' + 3 y = -1 sin(2 t) y_{1p} = Again using...

y_i=A{x_i}^b When I solve for A two different ways I am getting different answers..so somewhere I'm doing something wrong. If someone could point out where I would be grateful :). Using logs: y_i=A{x_i}^b ln(y_i)=ln(A)+b*ln(x_i) ln(y_i)-(ln(A)+b*ln(x_i))=r_i for least squares we want...

Homework Statement A box of textbooks of mass 24.6 kg rests on a loading ramp that makes an angle theta with the horizontal. The coefficient of kinetic friction is 0.23 and the coefficient of static friction is 0.35. A. As the angle theta is increased, find the minimum angle at which the...

solve y''+y'+y=cosx-x2ex y= yc+yp yc: characteristic eq gives r2+r+1=0 using quadratic formula i got r=-1/2+[(sqrt3)/2]i and r=-1/2-[(sqrt3)/2]i so yc=e-x/2(c1cos(sqrt3/2)x+c2sin(sqrt3/2)x but i have no idea of a particular solution that makes any sense. i tried a general...

Homework Statement For the following operator represented in the orthonormal basis {|1>, |2>} \hat{M} = \begin{pmatrix} 2 & i\sqrt{2} \\ -i\sqrt{2 & 2} \end{pmatrix} find the eigenvalues and eigenvectors and express them as a function of |1> and |2> normalized.The Attempt at a Solution I'm...

Homework Statement I'd like to use Parseval's equation to somehow express \sum a^{2}_{k} Homework Equations http://en.wikiversity.org/wiki/Fourier_series#Plancherel.27s_and_Parseval.27s_theorems At the bottom they have done that, but I'm not sure how they went from complex to real...

Homework Statement Sorry for doing another thread but I can't edit the old one any longer and I found out I made some calculation error but I'm pretty sure it's right now. The problem is to find the exact value of the series. Homework Equations \sum a_{k} The summation is to be done...

Homework Statement Calculate the exact value of the sum from minus infinity to infinity of Ck.Homework Equations Ck =...

Hi all, I understand the basic concept of undetermined coefficients, but am a little lost when g(t) in the equation yll+p(t)yl+q(t)y=g(t) is a product of two functions. The specific problem I'm working on is as follows: yll-2yl-3y=-3te-t When I solve for the homogeneous set of solutions I...

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...