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-rw-r--r--Problem Set 1.page10
1 files changed, 5 insertions, 5 deletions
diff --git a/Problem Set 1.page b/Problem Set 1.page
index 88ec240..d77e2eb 100644
--- a/Problem Set 1.page
+++ b/Problem Set 1.page
@@ -1,5 +1,5 @@
## Countability
-
+$\int f(x)$
1. Group the following sets according to their cardinality:
a. $\mathbb{N} = \{ 1,2,3,4,\dots \}$
@@ -25,10 +25,10 @@ Cook up other examples and post them on the wiki!
- $g(x) = x(x-2\pi)$ (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 $sin^4(x)$.)
+$\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 $sin^2(x)$:
+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 $
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 $