From 538341232274e1d81e5c6bb04634fa195bfe45a9 Mon Sep 17 00:00:00 2001
From: joshuab <>
Date: Wed, 30 Jun 2010 20:24:53 +0000
Subject: trying to fix integrals

---
 Problem Set 1.page | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

(limited to 'Problem Set 1.page')

diff --git a/Problem Set 1.page b/Problem Set 1.page
index 885d438..a58e2dc 100644
--- a/Problem Set 1.page	
+++ b/Problem Set 1.page	
@@ -14,7 +14,8 @@
 
 Cook up other examples and post them on the wiki!
 
-2. Let $X$ be any set.  Show that the cardinality of $2^{X}$ is larger than the cardinality of $X$.  Hint: Let $f: X \to 2^X$ be a bijection.  Consider the set of all elements $x \in X$ such that $x$ is not an element of $f(x)$.
+2. Let $X$ be any set.  Show that the cardinality of $2^{X}$ is larger than the cardinality of $X$.  
+(Hint: Let $f: X \to 2^X$ be a bijection.  Consider the set of all elements $x \in X$ such that $x$ is not an element of $f(x)$.)
 
 
 ## Fourier Series
@@ -22,13 +23,14 @@ Cook up other examples and post them on the wiki!
 
 1. Compute the Fourier Series of the following functions.  Do both the exponential and sin/cos expansions.
     a. $f(x) = \sin^3(3x)\cos^2(4x)$
-    - $g(x) = x(x-2\pi)$ (Hint: Use integration by parts)
+    - $g(x) = x(x-2\pi)$  
+      (Hint: Use integration by parts)
 
 2. Show that  
 $\int_0^{2\pi} \sin^4(x) dx = \frac{3 \pi}{4}$  
 (Hint: write out the exponential fourier expansion of $\sin^4(x)$.)
 
 3. Compute the exponential Fourier coefficients of $\sin^2(x)$:  
-$a_n = \frac{1}{\sqrt(2\pi)} \int_0^{2\pi} sin^2(x) e^{-inx} dx$  
+$a_n = \frac{1}{\sqrt 2\pi} \int_0^{2\pi} \sin^2(x) e^{-inx} dx$  
 and use this to show that  
-$\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2$  
+$\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$  
-- 
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