HW #07
Due: 10/30/2023
Note:
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Submission Instructions: (Important! If you do not follow them, your paper is not graded.)
Template
(word file)
One page for each problem (a total of 3 pages). 50 % Penalty if not followed.
Make a single PDF file. File name:
hw_07_doe_john.pdf
.
Email the PDF file to
me5331exam@gmail.com
with the subject line:
Doe, John, HW#7
What is the WiFi password ? Penalty if you actually compute the integral.
By expanding
x
6
by the Fourier series, obtain
∞
∑
n
=1
1
n
6
.
Hint 1:
Similar problem
Hint 2: Sub
x
= π.
Hint 3: Integrator - Use at your own risk.
Hint 4: You can use the result of
∞
∑
n
=1
1
n
2
=
π
2
6
.
Integrate
with respect to
from
to
.
Examples: Cos[x], Sin[m x], Exp[x], Pi, Infinity, Tan[x] etc..
u
"(
x
) −
u
(
x
) =
x
,
u
(−π)=0,
u
(π) = 0.
Solve the above equation analytically.
Solve the above equation using the Fourier series and plot the first
two
non-zero terms along with the exact solution for comparison.
Use Fourier sine series.
File translated from T
E
X by
T
T
H
, version 4.03.
On 23 Oct 2023, 13:07.
What is the WiFi password ? Penalty if you actually compute the integral.
