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-rw-r--r--Fourier Series.page8
1 files changed, 4 insertions, 4 deletions
diff --git a/Fourier Series.page b/Fourier Series.page
index 90a64f1..1ab9c43 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -1,8 +1,8 @@
-#Why Fourier series possible?</b>
+#<b>Why Fourier series possible?</b>
We first begin with a few basic identities on the size of sets. Show that the set of possible functions representing sets is not larger than the set of available functions?
-#Why Fourier series is plausible?</b>
+#<b>Why Fourier series is plausible?</b>
To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines:
$1.\quad\sin^2(x) = ?$
@@ -78,7 +78,7 @@ Summing these two functions we get the following:
<center>![$\cos^{2n}(x) + cos^{2n+1}(x)$](/cos10x-cos11x.gif)</center>
-#What is the Fourier series actually?</b>
+#<b>What is the Fourier Series actually</b>
##Initial Hypothesis
Now, to prove that the Fourier series is indeed true, we begin with the following hypothesis:
Let $f : \mathbb I \rightarrow \mathbb C$ be a continuous, periodic function where $I$ is some time interval(period of the function). Then it can be expressed as :
@@ -126,5 +126,5 @@ Extending this principle to the case of an n-dimensional vector:
--> don't quite remember this part
-#Why is Fourier series useful? </b>
+#<b>Why is Fourier series useful? </b>
Applications will be covered on Monday July 5, 2010. See you all soon! \ No newline at end of file