Coefficients Definition and 753 Threads

When you compute the Fourier series coefficients for a function, is there any quick way to check if your answer is correct or at least reasonable?Thanks.

Assignments given to me are drawn up in this manor: There is 1,34 mol of X, 1,69 mol of Y and 1,95 mol of Z at equilibrium. Calculate the equilibrium constant for the following reaction: 2X + Y_2 \rightleftharpoons 2XY or sometimes the coefficients are left out in the equilbrium equation...

Homework Statement Find the solution for y"+2y'+5y=(e^x)sinx Homework Equations The Attempt at a Solution So far I think I've gotten the solution from the characteristic equation, but I'm having trouble with the particular solution. For the characteristic equation solution...

for example 3 log (base5) 2 - (1/2)log (base5) 9 how would someone come to work this out i know that you are suppose to divide the 2nd part by the 1st but I am not sure where does the coefficients come in would that mean you multpily the coefficients

Hello! I have just a small question - does the theory of polynomials say something about their coefficients? I mean: is the polynomial with all the coefficients being imaginary still considered as a "normal' polynomial?

1. A 13,500 N car traveling at 50.0 km/h rounds a curve of radious 2.00m x 10 ^ 2. Find the following: A. the centripetal acceleration of the car (.965 m/s[2]) B. The centripetal force (13,500 N) C C. The minimum coefficient of static friction between the tires and the road that will allow...

Homework Statement ty' + y = \sin(t) state the following: Order of the DE 1st 2nd 3rd or n/a Linear Nonlinear Not Applicable Homogeneous Nonhomogeneous Not Applicable Constant Coefficients Variable Coefficients Not Applicable 2. The attempt at a solution...

Im just looking through examples of finding the Fourier coefficients. in one particular example bn is found to be = (-1/npi) (cosnpi - cos 0) then it says this is 0 when n is even and 2/npi when n is odd are we just substituting values of n e.g. 1,2,3... to find this result? i...

I have worked out how the connection coefficients enter into the expression for the Laplacian, for example, in different coordinate systems. Does anyone have general expressions for how the coefficients enter into other expressions such as divergence and curl and grad and so on? Thanks in...

Homework Statement This is the result of a problem from my Quantum class, but I figure it would be best to ask in here as my question is purely a question of how to solve a certain differential equation. the equation is of the form 0=Y''-i*a*Y' + b*Y where Y is a function of t So the...

Hi there, I am new member to this forum. I am taking online courses, in order to get my degree. For all of the problems, the transmission line in the problem has a characteristic impedance of 50 ohms and is one quarter wavelength (an electrical length of 90 degrees) at the frequency of the...

Homework Statement Solve the following initial value problem y'' - 5y' +6y = x*exp(2x), y(0) = y'(0) = 0 Homework Equations The Attempt at a Solution Ive found the complimentary solution to be r = 3, 2, Yg = C1*exp(3x) + C2*exp(2x) + Yp But to find Yp is giving me the...

Howdy, I got down Cramer's rule down fine, now I need to extend it to include equations that have complex coefficients. Do I let each matrix entry be something like, "5 + 2i" or is there something more than that? For example, say we have (2+3i)x + (5+3i)y + (9-6i)z = 10 + i (4+3i)x + (5-3i)y...

Can we use laplace transform to solve an ODE with variable coefficients? Like this one: 4x y" + 2 y' + y = exp (-x)

y" + 0.5y' + y = 1-cos(t); y(0) = y'(0) = 0 I used method of undetermined coefficients to get particular solution: Y(t) = -2sin(t) + 1 To get homogeneous solution, I solved characteristic equation to get complex roots: r_1,2 = -1/4 +- i*sqrt(15)/4 so homogeneous solution is: y...

Consider the step potential defined by V(x) = 0 if x < 0 Vb > 0 if x=> 0 a) Compute te relfection and tranmission coefficients for a particle of energy E > Vb approaching from th left For x < 0 Schrodinger equaion since V = 0 -\frac{\hbar^2}{2m} \frac{\partial^2 \psi}{\partial x^2}...

Let be the powe series: f(x)=\sum_{n=0}^{\infty}a(n)x^{n} then if f(x) is infinitely many times differentiable then for every n we have: n!a(n)=D^{n}f(0) (1) of course we don't know if the series above is of the Taylor type, but (1) works nice to get a(n) at least for finite n.

hello everyone, i need some huge help here. here's the equation : y''+y'-6y=10e^2x-18e^3x-6x-11. complementary solution:c1e^2x+c2e^-3x s1={e^2x} s2={e^3x} s3=(x,1} ok since e^2x exists in the complimentary solution, it is therefore a solution, so i multiply it by x to get s'1{xe^2x}...

Suppose that the coefficients of static and kinetic friction have values such that the static coefficient is twice the value of the kinetic coefficient for a crate in contact with a cement floor. Does this mean that the magnitude of the static frictional force acting on the crate at rest would...

this problem has been bugging me for a few weeks now and here it is A=\sum_{k=0}^{\infty}\sum_{m=-N}^{+N}a_k\cos(\frac{mk\pi}{N+1})\cos(\frac{mj\pi}{N+1})=1 what i am trying to do is find the a_k terms. i've tried a couple of different ways but there just seems to be too many different...

Yes, another thread... lab due tomorrow :-p We take the integral of the function f(t) times one of the components: integral(0->T) of [a0 + sigma(n=1->N) acos(nwt) + bsin(nwt)]sin(nwt) Now, in order to evaluate this is it correct to say we multiple sin(nwt) through then take the integral of...

Is there a website that has these? The NASG database doesn't list values, just a plot (not the best way to read values!). The .dat file with each polar curve seems to only be lift, drag, and AoA. Any help is appreciated!

Hi all, I can't figure out where I've doing mistake in this quite simple problem: y''' - y = x^3 - 1 FSS = [e^{x}, e^{-\frac{1}{2}x} \cos \left(\frac{\sqrt{3}}{2}x\right), e^{-\frac{1}{2}x} \sin \left(\frac{\sqrt{3}}{2}x\right)] Then, because on the right side there is...

for this question: calculate the mass and linear absorption coefficients of air for Cr K(alpha) radiation. Assume that air contains 80 percent nitrogen and 20 percent oxygen by weight and has a density of 1.29*10^(-3) g/(cm^3) my problem: i have no idea where to start.

What is the coefficient of drag, Cd, of a tennis ball (roughly d = 6,5 cm, m = 57 g)? Generally; where do I find such coefficients? I'd like to find coefficients for projectiles in water too - since these are supposedly not the same, because of the water viscosity. I've found the "Drag...

I know how to solve the following ODE with variation of parameters: y''+4y=4\sec{\left(2t\right)}. Is there any way to solve this with undetermined coefficients? So far I have tried Yp=Acos(2t)+Bsin(2t), but that didn't work. Thanks for the help.

I need to find the Fourier series for the function f(x)=x. I have come across trying to find the integral from -pi to pi of -ixSin(nx). How do I go about evaluating this integral when n is infinity? I seem to only be able to find integrals in an integral table where n is an integer, but not...

y''+16y=24cos(4x) it was mentioned in class that our book's answer was wrong on some problem, but I forgot which one and now that's biting me in the butt(I really should've written it down) For the particular solution I got y=3x*sin(4x), which if I plug it in works. The book's solution...

hi all i have a bit of a problem here, it has to do with completing the cube. here is the problem y''' +y' + 2y = 0 i am trying to sove by the methoed of constant coefficients

Hi, this is my first post. Right now I am in grade 12 advanced functions and introductory calc. I have just started the second unit which is polynomial equations and inequalities. I am currently having a problem with comparing coefficients. I understand up until where you find the...

This is the question I am working on: An adult is pulling two small children in a sleigh over level snow. The sleigh and children have a total mass of 47 kg. The sleigh rope makes an angle of 23 degrees with the horizontal. The coeffcient of friction between the sleigh and the snow is 0.11...

An experimenter wishes to investigate the effect of three variables, pressure, temperature, and the type of catalyst, on the yield in a refining process. If the experimenter intends to use three temperature settings and three pressure settings and two types of catalysts, how many experimental...

Sup' all? Ok, I have a quick question (hopefully). I'm trying to use the method of undetermined coefficients, and I keep getting stuck at one specific spot in the method. I'm not exactly sure what I'm doing. Let me try and explain: The problem is given as: 2y''+3y'+y=t^2+3*\sin t Which...

k, maybe wrong forum... whatever... Anyway, so i was hoping someone could maybe derive or at least explain binomial coefficients. Like, i know that binomial(n,r)= n!/(n-r)!r! but why? in class the guy was explaining something like, if you're counting, and you're trying to arrange 3 balls into...

Find all solutions \phi of y''+y=0 satisfying: 1) \phi(0)=1, \phi(\pi/2)=2 2) \phi(0)=0, \phi(\pi)=0 3) \phi(0)=0, \phi'(\pi/2)=0 4) \phi(0)=0, \phi(\pi/2)=0 I cannot seem to solve parts 2-4 in a way that...

I am working through a mathematics olympiad problem book, and I am asked to prove that n choose r, where n is the row number and r is the term number in the row is equal to that term. Can someone please give me a hint? I have not been able to find ANY proofs on the internet through a basic...

Let SL(2,Z) be the set of 2x2 matrices with integer coefficients. I know that SL(2,Z) is generated by S and T, where S= (0 -1 1 0) and T= (1 1 0 1). But how can I show that everyone element of G (the group generated by S and T) is in SL(2,Z)? Also, let...

Ok, so the wire used in an electromagnet will likely have its resistance affected by a temp change on a PTC and thus require a higher voltage to maintain power, simple enough. But will an electromagnet also suffer temp coefficients for induction and coercivity and have a currie temp too?

Hello, I have this DE: y'' + 2y' - 3y = 8ex - 12e3x when I find homogeneous solution I get yh = c1ex + c2e-3x; so now to find the particular solution by method of undetermined coefficients, do I set y to smth like this: y = y1 + y2 where y1 = Axex, y2 = A3x ? since one...

I'm working in Liboff, 4e, QM, page 114, problem 4.35. An electron in a 1-D box with walls at x= 0,a is in the state \psi(x) = A for x\in (0,a/2) and \psi(x) = -A for x\in (a/2,a). What is the lowest possible energy that can be measured? From my understanding, the answer to this question...

(d^2x/dt^2)+(w^2)x=Fsin(wt), x(0)=0,x'(0)=0 Hope that's readable. First part is second derivative of x with respect to t. w is a constant and F is a constant. I need to find a solution to this using method of undetermined coeffecients and I'm confused with all the different variables. Anyone...

I have been taught that the equation Ax^2 + Cy^2 +Dx + Ey +F = 0 represents a general form of conics. Then the conditions of the coefficients in the equation could identify which type of conics the equation represents... Circle: A=C Ellipse: A does not=C and AC>0 Hyperbola: AC<0 and...

In dealing with solutions to the Schroedinger equation, I have come across the so-called expansion coefficients (c n ). I have read that the square of the coefficient is the probability density of an allowed value of E. How is there a probability of any given value of E? I know that in a...

Okay. so i have a problem that I'm finding tricky to work backwards from. I'm given the coefficients Period 4 and x(t) is continuous. a_{k} = 0 if k=0 a_{k} = j^k*sin(k*Pi/4)/(k*Pi) if k!=0 Supposed to find x(t). Now I've tried a few things but have come up with many different...

An apparatus to determine coefficients of friction is shown above. The box is slowly rotated counterclockwise. When the box makes an angle (Theta) with the horizontal, the block of mass m just starts to slide, and at this instant the box is stopped from rotating. Thus at angle(Theta), the block...

I've looked in my textbook and asked my fellow classmates, but I have had no luck in figuring out how to derive these coefficients. Can anyone tell me how I would go about doing this?

My question is about the coefficients of a complex laurent series. As far as I know, there are three kinds of series: those which converge in a finite circular region around the expansion point z0,(aka taylor series), those that converge in a ring shaped region between two circles centered at...

Try this problem: A skier traveling 11 m/s reaches the foot of a steady upward 17 degree incline and glides 12 meters upward along this slope before coming to rest. Calculate the average coefficient of friction. I've tried using the Conservation of energy theorem, but it is not working. Is...

Someone know the coefficients of friction of wood in wood, wood in metal, metal in wood and metal in metal, calculated with the tangent of the resulting angle of the inclined plane method?

Hi! I have to calculate the Fourier coefficients c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx and the Fourier series for the following function: f(x)= \begin{cases} \frac{2}{\pi}x + 2 & \text{for } x\in \left[-\pi,-\pi/2\right]\\ -\frac{2}{\pi}x & \text{for } x\in...