From 80b88017e4028a93a70b73169aa855047ff7c8b5 Mon Sep 17 00:00:00 2001
From: siveshs <siveshs@gmail.com>
Date: Sat, 3 Jul 2010 04:25:00 +0000
Subject: section 3 editing

---
 Fourier Series.page | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

(limited to 'Fourier Series.page')

diff --git a/Fourier Series.page b/Fourier Series.page
index ddcd3f4..fef0cc2 100644
--- a/Fourier Series.page	
+++ b/Fourier Series.page	
@@ -121,9 +121,14 @@ In order to prove orthonormality of the basis vectors:
   
 $$
 \begin{array}{ccl}
-(f_n,f_m) = \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \bar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\
+(f_n,f_m) & = & \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \bar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\
 & = & \frac{1}{2\pi} \, \int_0^{2\pi} \, e^{i(n-m)x} \, dx \\
-Here, n = m \Rightarrow (f_n,f_m) & = & 1\\
+\end{array}
+$$  
+Here,  
+$$
+\begin{array}{ccl}
+n = m \Rightarrow (f_n,f_m) & = & 1\\
 n \neq m \Rightarrow (f_n,f_m) & = & 0\\
 \end{array}
 $$  
-- 
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