From f12ef31ef71c32ff3a8071595cf27eff4322477d Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 03:25:52 +0000 Subject: still testing --- Fourier Series.page | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/Fourier Series.page b/Fourier Series.page index a050d70..fb9ed7e 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -4,10 +4,9 @@ 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: - $1. \cos(2x) = 1 - 2 \sin^2(x)$ $$\begin{array}{ccl} -e^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ +\sin^2(x) & = & ?\\ & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$$ -- cgit v1.2.3