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Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
74 Applied calculus of variations for engineers
The coefficient of the solution is also a straightforward generalization as
c
mnr
=
8
abc
c
0
b
0
a
0
f(x, y, z)sin
mπx
a
sin
nπy
b
sin
rπz
c
dxdydz.
These last two solutions were the analytic solutions to the two- and three-
dimensional heat conduction problems. The computational solution of the
two-dimensional problem will be further addressed in Chapter 12.
Let us now solve a problem of two spatial variables again, but with a tem-
poral variable whose second derivative is present:
h
2
(
2
u
∂x
2
+
2
u
∂y
2
)=
2
u
∂t
2
.
We assume constant boundary conditions:
u(0,y,t)=u(a, y, t)=0,
and
u(x, 0,t)=u(x, b, t)=0.
The a, b are the dimensions ...
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Publisher Resources

ISBN: 9781482253597