From 6b5ae3708f3636f0d07a92cad1c3cb0ac32744e2 Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 23:18:48 +0000 Subject: section 3 editing --- Fourier Series.page | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/Fourier Series.page b/Fourier Series.page index 8ef6bd3..ab344fd 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: $1.\quad\sin^2(x) = ?$ @@ -78,9 +78,9 @@ 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? Now, to begin proving that the Fourier series is a true fact let us begin with the following hypthesis: -Let f ____ be a continuous, periodic function where I is some the time interval(period of the function). Then it can be expressed as +Let f ____ be a continuous, periodic function where I is some the time interval(period of the function). Then it can be expressed as : $$ \begin{array}{ccl} @@ -88,5 +88,6 @@ f & = & \Sigma e^{inx}\\ & = & a0 + \Sigma a~n\cos nx + \Sigma b~n\sin nx\\ \end{array} $$ - -##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