- #1
member 428835
Homework Statement
i am solving the heat equation and so far i know what i have is correct. basically, i am down to this [tex]\sum_{n=0}^{\infty}A_n\cos(\frac{n\pi x}{L})=273+96(2L-4x)[/tex] where all i need is to solve for [itex]A_n[/itex]
The Attempt at a Solution
i was thinking about taking advantage of the orthogonality of the cosine function and multiplying both sides by [itex]\cos(\frac{m\pi x}{L})[/itex] and then integrate over the interval [itex][0,L][/itex]. my question is, if [itex]m\neq n[/itex] then i can move this cosine into the sum, integrate term wise, yet the left side equals zero ([itex]m\neq n[/itex]). Thus, [itex]m = n[/itex], and then if i multiply both sides by [itex]\cos(\frac{n\pi x}{L})[/itex] i cannot put this cosine term inside the sum, and thus i have lost the idea of how to solve for [itex]A_n[/itex]. any help/advice is awesome!
for what it's worth, this is not a class i am in, I'm just doing the problem for fun. thanks for your help!