Solve the heat problem on the circle u_t = ku_{xx} u(x,0) = phi(x) where phi(x) is the 2l periodic extension of phi using the separation of variables. I am able to go as far as u = XT -X''/X = lambda where lambda = beta^2 usually the solution for X'' + beta^2 * X = 0 is Ccos(beta * L) + D sin ...continues
Fourier Series and Heat Equations
Please see the attached file for the fully formatted problems.
Sine to cosine to exponents transition in Fourier analysis.
Could one please explain the sin-cos to exponents transition in Fourier analysis?
So I am able to get to u(x,t) = sum_{n=-infty}^{infty} Cexp(iBx - ktB^2) + Dexp(-iBx - ktB^2) because the general series is sum_{n=-infty}^{infty} X(x)T(t) You have 1 coefficient in your general series, yet I have 2. How do I get it into 1?
Waveforms : Fourier and Laplace Transforms
Have the following question regarding extracting information from a waveform a. Write down an expression, in the time domain, for the signal in the diagram above. b.Derive the Laplace transform for this signal. c.Use Laplace transform analysis to derive the Fourier transform in its simplest form. All details in the a ...continues
1. Find the Fourier sine series of f(x)=1, 0
Could you please show me how to do the problem attached? You don't have to do the first part (proving solutions to the wave equation by a separation of variables) as I know how to do that. Please start where it asks what is a normal mode, etc... Thank you.
see attachment.....please show each step in detail in the solution. Let f(theta) be a continuous function on the interval...and let fn(theta)denote its nth Fourier series approximant....
Find the fundamental period p and corresponding w...
Find the fundamental period p and corresponding w of: 1) 12sin(4pi x) 2) 3cos(7pi x) 3) 12sin(4pi x)+3cos(7pi x) recall: w=2f pi =2pi/p Help needed: How would i solve these problems?
Find the 7 Fourier coefficients of the function...
There is an attached file with further information regarding the problem. Find by inspection the first seven Fourier coefficients {a0, a1, b1, a2, b2, a3, b3} of the function: f(x) = 14-cos(Pi*x/10) + 3sin(Pi*x/10) + 0.5cos(Pi*x/5) + 5sin(3*Pi*x/10)
