HW #06
Due: 10/27/2025
1
.
What is the 10 digit WiFi password? Penalty if you actually compute the integral.
2.
By expanding
x
4
by the Fourier series, obtain
∞
∑
n
=1
1
n
4
.
Hint: You can use the result of
∞
∑
n
=1
1
n
2
from
#14 lecture
Integrate
with respect to
from
to
.
Examples: Cos[x], Sin[m x], Exp[x], Pi, Infinity, Tan[x] etc..
3.
Solve the following differential equation using the Fourier series and plot the first
three
non-zero terms over −π <
x
< π.
u
"(
x
) =
f
(
x
),
u
(−π)=0,
u
(π) = 0,
where
f
(
x
) =
⎧
⎪
⎨
⎪
⎩
−1
−π <
x
< 0
1
0 <
x
< π.
File translated from T
E
X by
T
T
H
, version 4.03.
On 19 Oct 2025, 21:05.
What is the 10 digit WiFi password? Penalty if you actually compute the integral.
