Recent content by RayonG

According to my professor, LCKurtz was right. The solution is f(x)=u(x,0)=\sum_{n=1}^{\infty}b_n*sin((n+0.5)x) where B_n=(2/\pi)\int_{0}^{\pi}f(x)*sin((n+0.5)x)dx. As far as deriving b_n, my professor told me it was a guess. I suppose he'll teach us later on or something.

Thanks for the input! As of right now, I'll just write down what I can (it's only a homework problem). I'll ask my professor on Monday (perhaps he is using this problem as a direct link to teaching us the Sturm Liouville theory).

Do you mean that X'(x)=cos((n-0.5)x) and so X(x)=sin((n-0.5)x)? T_n(t) would be Ce^((λ_n)t). And no, I have not learned Sturm-Liouville expansions, so I'm taking a guess that B_n is the Fourier sine series...

I realized that my edit was incorrect. I corrected with my next post. I'm also new to this forum, and forgive me since I meant ∏ to be equal to \pi. Since cos(μ\pi)=0. μ\pi=n\pi+\pi/2 where n=positive integer. Then I get, X(x) = Bsin((n+0.5)x). I don't know if I'm doing this right...

So now I have X(x)=sin((n+0.5)x) where n is a positive integer. Using u_n(x,t)=\sum_{n=1}^{\infty}b_n*T_n(t)*X_n(x) and plug in t=0, So u(x,0)=f(x)=\sum_{n=1}^{\infty}b_n*sin((n+0.5)x). Now does b_n = the Fourier sine series?

Homework Statement Find a formal solution of the heat equation u_t=u_xx subject to the following: u(0,t)=0 u_x(∏,t)=0 u(x,0)=f(x) for 0≤x≤∏ and t≥0 Homework Equations u(x,t)=X(x)T(t)The Attempt at a Solution I first began with a separation of variables. T'(t)=λT(t) T(t) =...