From 9e3e94605efade2381276aaa1e83f95ad8e7b8fd Mon Sep 17 00:00:00 2001 From: eggy Date: Tue, 21 Nov 2023 22:05:00 -0500 Subject: [PATCH] ece205: fix bug --- docs/2a/ece205.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/2a/ece205.md b/docs/2a/ece205.md index b5661b8..5bb7073 100644 --- a/docs/2a/ece205.md +++ b/docs/2a/ece205.md @@ -395,7 +395,7 @@ Thus if a Fourier series on $(0,L)$ exists, it can be expressed as either a **Fo We have $L=\pi,a=\sqrt 2$. \begin{align*} - u(x,t)&=\sum^\infty_{n=1}\alpha_ne^{left(\frac{n\pi\sqrt 2}{\pi}\right)^2t}\sin(\frac{n\pi x}{\pi}) + u(x,t)&=\sum^\infty_{n=1}\alpha_ne^{\left(\frac{n\pi\sqrt 2}{\pi}\right)^2t}\sin(\frac{n\pi x}{\pi}) &=\sum^\infty_{n=1}\alpha_ne^{-2n^2t}\sin(nx) \\ \alpha_n&=\frac 2 L\int^L_0f(x)\sin(\frac{n\pi x}{L})dx \\ &=\frac2\pi\int^{\pi/2}_0\frac\pi 2\sin(nx)dx+\frac2\pi\int^\pi_{\pi/2}(x-\frac\pi2\sin(nx)dx \\