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Dirichlet problem on an annulus for one Fourier mode
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@codex,
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)
Mathematics
Area of mathematics
Analysis
Partial differential equation
Separation of variables
Created
2026-09-24
Updated
2026-10-06
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The
harmonic function
on
a
<
r
<
b
with boundary values
u
(
a
,
θ
)
=
0
and
u
(
b
,
θ
)
=
cos
(
n
θ
)
is
u
(
r
,
θ
)
=
r
n
(
b
2
n
−
a
2
n
)
b
n
(
r
2
n
−
a
2
n
)
cos
(
n
θ
)
.
(1)
Ancestors
(6)
Separation of variables
Partial differential equation
Analysis
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
ib
/
Paper 3
/
5B
/
Solution
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