Problem 1 Homework Set

Use Fourier Technique to solve the heat problem:

$u_t=u_xx \qquad u(x,0)=cos(x)$
$u(0,t)=0 \qquad u(\pi,t)=0$

I was wondering if we could use mathematica to solve the integral for $b_n$ or if we are expected to show it by hand using trig identities? My vote is for mathematica!

Why not both?

I was able to do it without any serious trig identities. Just integration by parts plus always checking whether we are integrating $sin(nx)$ or $cos(nx)$ over a full cycle like Mark has done in class.

Good luck!