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authorOpheliar99 <>2010-07-04 04:12:42 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-04 04:12:42 +0000
commitf0c461bce6678793f61c2e0c7fafd8b1801129f6 (patch)
treee0509520d752c0e14e94e3f82213f607bbf15b94
parent14244b4506f772541be6b2289b2ace8651d0e7f1 (diff)
downloadafterklein-wiki-f0c461bce6678793f61c2e0c7fafd8b1801129f6.tar.gz
afterklein-wiki-f0c461bce6678793f61c2e0c7fafd8b1801129f6.zip
posted solutions of 2 and 3 in pset2
-rw-r--r--Problem Set 2.page2
1 files changed, 1 insertions, 1 deletions
diff --git a/Problem Set 2.page b/Problem Set 2.page
index 2d5a503..667abad 100644
--- a/Problem Set 2.page
+++ b/Problem Set 2.page
@@ -41,7 +41,6 @@ $\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$
2. Since
$\sin x = \frac{e^{ix}-e^{-ix}}{2}$,
-
$\sin^4 x = \frac{{( e^{ix}-e^{-ix} )}^4}{16}$
$= \frac{e^{i 4x}+e^{-i 4x}-4 e^{i 2x} -4 e^{-i 2x}+6}{16}$.
@@ -56,6 +55,7 @@ $a_{-4} = a_{4} = \sqrt{2\pi} \times 1/16$, $a_{-2} = a_{2} = - \sqrt{2\pi} \tim
Since $a_m = < f_m, f >$,
+
$\int_0^{2\pi} \sin^4(x) dx = <1, f> = \sqrt{2\pi} \times < f_0, f >$
$= \sqrt{2\pi} \times a_0 = \frac{3 \pi}{4}$