HW #08
Due: 11/06/2023
Note:
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Template
(word file)
One page for each problem (a total of 2 pages). 50 % Penalty if not followed.
Make a single PDF file. File name:
hw_08_doe_john.pdf
.
Email the PDF file to
me5331exam@gmail.com
with the subject line:
Doe, John, HW#8
1.
Solve
u
"(
x
) −
u
(
x
) = −
w
(
x
), − ∞ <
x
< ∞
by the Fourier transform method. You can leave out
w
(
x
) as it is.
Hint:
⌠
⌡
∞
−∞
cos ω
x
1 +
x
2
d
x
= π
e
−|ω|
.
2. Solve the following integral equation for
u
(
x
).
⌠
⌡
∞
−∞
u
(
x
−
y
)
u
(
y
)
d
y
=
e
−
x
2
.
Hint:
F
(
e
−
a
x
2
) =
⎛
√
π
a
e
−ω
2
/(4
a
)
.
File translated from T
E
X by
T
T
H
, version 4.03.
On 29 Oct 2023, 07:49.
