I enclose Maple general solution to the PDF heat equation in 1 dimention.
I need corrections of it to enable me to calculate the heat equation in certain conditions :
du(x,t)/dt - d^2/x,t)/dx^2 = ; t>0, x belongs to interval [0,phi[
with boundary conditions :
u(x,0) = sin(x)cos^2(x) ; x belongs to interval [0, phi)
u(0,t) = 0
u(phi,t) = 0 ; t is still t>0
Heat equation in a rod in 1 dimention
> with(plots):animate(plot, [u(x,t), x=0..Pi, thickness=2], t=0..4, frames=50);
Question 2 :
How to calculate Fourier coefficients n natural number i.e. n belongs to Z
for the function f(x) = sin(x)cos^2(x) on the onterval from - phi to phi.
How to do it ? Perhaps changes to this code :
Calculate and plot serial part sums for Fourier series given by function g1 and g2
on the interval for g1: [- ,0] and for g2 : [0, ].
> c:=(n,g1,g2)->(2*Pi)^(-1)*int(g1*exp(-I*n*x), x=-Pi..0)+(2*Pi)^(-1)*int(g2*exp(-I*n*x), x=0..Pi);