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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
4
Higher order derivatives
The fundamental problem of the calculus of variations involved the first deriva-
tive of the unknown function. In this chapter we will allow the presence of
higher order derivatives.
4.1 The Euler-Poisson equation
First let us consider the variational problem of a functional with a single func-
tion, but containing its higher derivatives:
I(y)=
x
1
x
0
f(x, y, y
,...,y
(m)
)dx.
Accordingly, boundary conditions for all derivatives will also be given as
y(x
0
)=y
0
,y(x
1
)=y
1
,
y
(x
0
)=y
0
,y
(x
1
)=y
1
,
y

(x
0
)=y

0
,y

(x
1
)=y

1
,
and so on until
y
(m1)
(x
0
)=y
(m1)
0
,y
(m1)
(x
1
)=y
(m1)
1
.
As in the past chapters, we introduce an alternative solution
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Publisher Resources

ISBN: 9781482253597