From 5c698a3abf0fd7fb17dacea37ca5076ce460b38e Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 03:26:51 +0000 Subject: still testing --- Fourier Series.page | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) (limited to 'Fourier Series.page') diff --git a/Fourier Series.page b/Fourier Series.page index 6159544..204d0f4 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -5,9 +5,8 @@ We first begin with a few basic identities on the size of sets. Show that the se ##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: -$$ -\sin^2(x) = ?\\ -\begin{array}{ccl} +$$\sin^2(x) = ?$$ +$$\begin{array}{ccl} & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$$ -- cgit v1.2.3