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-rw-r--r--Problem Set 1.page22
1 files changed, 11 insertions, 11 deletions
diff --git a/Problem Set 1.page b/Problem Set 1.page
index a68109f..eb2c6e7 100644
--- a/Problem Set 1.page
+++ b/Problem Set 1.page
@@ -2,15 +2,15 @@
1. Group the following sets according to their cardinality:
- - $\mathbb{N} = \{ 1,2,3,4,\dots \}$
- - $\mathbb{Z} = \{ \dots, -2, -1,0,1,2, \dots \}$
- - $\mathbb{N} \times \mathbb{N}$
- - $\mathbb{Q}$ = Set of all fractions $\frac{n}{m}$ where $n,m \in \mathbb{Z}$
- - $\mathbb{R}$
- - $(0,1)$
- - $2^{\mathbb{N}}$ = Set of all subsets of $\mathbb{N}$.
- - $2^{\mathbb{R}}$ = Set of all subsets of $\mathbb{R}$.
- - $\mathbb{R}^{\mathbb{R}}$ = Set of all functions from $\mathbb{R}$ to itself.
+ a. $\mathbb{N} = \{ 1,2,3,4,\dots \}$
+ - $\mathbb{Z} = \{ \dots, -2, -1,0,1,2, \dots \}$
+ - $\mathbb{N} \times \mathbb{N}$
+ - $\mathbb{Q}$ = Set of all fractions $\frac{n}{m}$ where $n,m \in \mathbb{Z}$
+ - $\mathbb{R}$
+ - $(0,1)$
+ - $2^{\mathbb{N}}$ = Set of all subsets of $\mathbb{N}$.
+ - $2^{\mathbb{R}}$ = Set of all subsets of $\mathbb{R}$.
+ - $\mathbb{R}^{\mathbb{R}}$ = Set of all functions from $\mathbb{R}$ to itself.
Cook up other examples and post them on the wiki!
@@ -21,8 +21,8 @@ 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.
-- $f(x) = sin^3(3x)cos^2(4x)$
-- $g(x) = x(x-2\pi)$ (Hint: Use integration by parts)
+ a. $f(x) = sin^3(3x)cos^2(4x)$
+ - $g(x) = x(x-2\pi)$ (Hint: Use integration by parts)
2. Show that
$ \int_0^{2\pi} sin^4(x) dx = \frac{3 \pi}{4} $