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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
12-42 Mathematical Methods
Ans:
22
1
81
( , ) sin sin cos .
2
n
Cnnxnat
yxt
ll
n
=
=
pp p
p
(c) Initial velocity:
3
() sin
x
gx b
l
=
p
Ans:
33
( , ) 9sin sin sin sin .
12
bl x at x at
gxt
allll
⎡⎤
=−
⎢⎥
⎣⎦
pp p p
p
(d) Initial velocity:
32
() sin cos
xx
gx b
ll
=
pp
Ans:
55
( , ) sin sin sin sin
.
25
bl x at bl x at
yxt
alla l l
=+
pp p p
pp
12.13.9 Laplace’s Equation or
Potential Equation or Two-
dimensional Steady-state
Heat Flow Equation
The two-dimensional heat conduction equation is
given by
22
,
u
au
t
=
where
22
2
22
xy
∂∂
=+
∂∂
is the
Laplacian operator
In the case of steady-state heat fl ow
∂∂=/0ut
and
equation reduces to
22
2
22
0
uu
u
xy
∂∂
=+=
∂∂
The solution u(x, y ) of the above equation ...
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Publisher Resources

ISBN: 9781299446557Publisher Website