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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
62 Applied calculus of variations for engineers
Subtracting the equations and canceling the identical terms results in
(λ
2
λ
1
)

D
u
1
u
2
dxdy =0.
Since
λ
1
= λ
2
,
it follows that

D
u
2
u
1
dxdy =0
must be true. The two eigensolutions are orthogonal. With similar arguments
and specially selected auxiliary functions, it is also easy to show that the sec-
ond solutions also satisfy
Δu
2
λ
2
u
2
=0.
The subsequent eigensolutions may be found by the same procedure and
the sequence of the eigenpairs attain the extrema of the variational problem
under the successive conditions of the orthogonality against the preceding so-
lutions.
5.3 Sturm-Liouville problems
The process demonstrated ...
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Publisher Resources

ISBN: 9781482253597