section 3 editing

1 files changed, 8 insertions, 3 deletions

diff --git a/Fourier Series.page b/Fourier Series.page
index 0909384..a2a18aa 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -178,8 +178,13 @@ $$ a_m = \int_0^{2\pi} \, f \, \frac{1}{\sqrt{2\pi}} \, e^ {-inx} \, dx $$
 This is the common definition for the terms of the Fourier series.
 
 ##Proving that this function is does indeed completely represent $f$
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---> don't quite remember this part
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+It is important to note at this point that we have simply expressed the periodic function $f$ in terms of a sum of arbitrary orthonormal vectors $f_n$. We haven't quite shown yet that the sum of orthonormal vectors actually completely represents $f$. Put in another way, there could be some components of $f$ that are not described by the vectors $f_n$. It is necessary to prove first that no other such components exist.
+  
+--> don't quite remember this part  
+  
+Now, we know that the entire function space can be described by the defined basis vectors. We can now prove that, the sum of terms that we computed in the previous section does indeed converge to $f$ as follows:
+  
+--> don't quite remember this part    
+  
 #<b>Why is Fourier series useful? </b>
 Applications will be covered on Monday July 5, 2010. See you all soon!  
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