From 0af3824b67e5cb4f47121076dba710fd3c413f59 Mon Sep 17 00:00:00 2001 From: siveshs Date: Sat, 3 Jul 2010 03:52:28 +0000 Subject: section 3 editing --- Fourier Series.page | 8 ++++---- 1 file 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? +#Why Fourier series possible? 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? +#Why Fourier series is plausible? 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:
![$\cos^{2n}(x) + cos^{2n+1}(x)$](/cos10x-cos11x.gif)
-#What is the Fourier series actually? +#What is the Fourier Series actually ##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? +#Why is Fourier series useful? Applications will be covered on Monday July 5, 2010. See you all soon! \ No newline at end of file -- cgit v1.2.3