Hi everyone,
So I have to solve a ODE (for dy/dt = K*(y-s) ) numerically in Matlab.
This is how I set it up:
K = 1;
s = 20;
y0 = 100;
npoints = 50;
dt = 0.1;
y = zeros(npoints,1); % this initializes the vector y to being all zeros
t = zeros(npoints,1);
y(1) = y0; % the...
Hi,
Here is the equation:
x+x'=5.1sin(600*t)*u(t)
Our teacher gave us a hint that we should try using a substitution which is a system of sines, cosines, and looks something similar to 5.1sin(600*t)*u(t).
I tried substituting:
x(t)= A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)...
I am pretty sure about the series. I verified with the back of the book. We were also supposed to show pi^2/12=1-1/2^2+ etc. I plugged in x=o and was able to prove it.
For the pi^2/6, I tried setting x to be pi/2 so that the cosine term goes away but that didn't work out.
I didn't want to type out the Fourier series since I am really new to latex but here it is
f(x) =pi^2/6 +\Sigma { (2(-1)^n/n^2) cos nx + ((-1)^(n+1) pi/n + 2/(pi * n^3) [(-1)^n-1] sin nx }
I hope that made sense and that I didn't make any typos.
Homework Statement
f (x) = 0 -pi<x<0
x^2 0<x<pi
Find the Fourier series and use it to show that
(pi^2)/6=1+1/2^2+1/3^2+...
Homework Equations
N/A
The Attempt at a Solution
I was able to find the Fourier series and my answer matched with the back of the...
Here is a sample question:
What are the Fourier coefficients of the function f(x)=ae^(-ix)+b+ce^(ix)? And express the norm in terms of Fourier coefficients.
They don't mention if it is the L^2 norm or not.
Hi,
I was wondering if it is possible to express the norm of a function in terms of Fourier coefficient. If so, how do you go through it if given a particular function.
Thanks