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a
a
α
Figure 34: Domain for problem 2 of 7.4
2.
The analysis is more involved when the equation is NOT separable in coordinates suitable
for the boundary. Only two nonseparable cases have been solved in detail, one for a boundary
which is an isosceles right triangle.
The function
sin
µπx
a
sin
νπ
a
y
is zero along the
x
and
y
part of the boundary but is not zero along the diagonal side.
However, the combination
sin
µπ
a
x
sin
νπ
a
y
∓
sin
µπ
a
y
sin
νπ
a
x
is zero along the diagonal if
µ
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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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