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1/4
1
φ
= 0
φ
x
= 0
φ
= 0
φ
y
= 0
Figure 33: Domain fro problem 1 of 7.4
1.
ϕ
(
x, y
)=
XY
X
0
Y
+
XY
0
+
λXY
=0
X
0
X
=
−
λ
−
Y
0
Y
=
−
µ
X
0
+
µX
=0
Y
0
+(
λ
−
µ
)
Y
=0
X
(0) =
X
0
(1) = 0
Y
(0) =
Y
0
(1
/
4) = 0
⇓⇓
X
n
=s
in
(
n
−
1
2
)
πx
Y
nm
=s
in(
m
−
1
2
)4
πy
µ
n
=
h
(
n
−
1
2
)
π
i
2
λ
nm
=
h
(
n
−
1
2
)
π
i
2
+[
(4
m
−
2)
π
]
2
n
=1
,
2
,
···
m
=1
,
2
,
···
ϕ
nm
=s
in(
n
−
1
2
)
πx
sin (4
m
−
2)
πy
λ
nm
=[
(
n
−
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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