From 8c7d2e6af68b04e0e33842c2aa052c20dcfb0506 Mon Sep 17 00:00:00 2001 From: siveshs Date: Sat, 3 Jul 2010 05:30:23 +0000 Subject: editing --- Fourier Series.page | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/Fourier Series.page b/Fourier Series.page index 1bd52f4..8010928 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -12,7 +12,9 @@ We first begin with a few basic identities on the size of sets. Then, we will sh --> don't have the notes for this ## Proof that no. of available functions is greater than number of functions required to define the periodic function ---> don't have the notes for this +Consider any arbitrary periodic function in the interval $[-\pi,\pi]$. This can be represented as a series of values at various points in the interval. For example, +$ f(0) = ... , f(0.1) = ..., f(0.2) = ... $ and so on. At each point, we can assign any real number (i.e. $\in \mathbb R$). So, the number of possible periodic functions in an interval is of the order of $\mathbb R^{\mathbb R}$. +--> don't quite remember how this goes. #Why Fourier decomposition 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: -- cgit v1.2.3