Skip to Main Content
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
Analytic solutions of variational problems 79
Let us now consider simply using pre-computed complete integrals. Cer-
tain complete integral solutions actually contain integrals. Consider the non-
homogeneous differential equation type with non-constant coefficients
a(x)(
∂u
∂x
)
2
+ b(x)(
∂u
∂y
)
2
= f (x)+g(y).
Such problems have a complete integral solution of
u(x, y)=
x
f(t)+a
1
a(t)
dt +
y
g(t) a
1
b(t)
dt + a
2
.
For example, the equation
(
∂u
∂x
)
2
+(
∂u
∂y
)
2
= x + y
has a complete integral solution of the form
u(x, y)=
x
t + a
1
dt +
y
t a
1
dt + a
2
.
There are also rather specific, but practical problems where the partial deriva-
tives occur in an exponential expression. The ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Calculus of Variations for Engineers, Third edition, 3rd Edition

Applied Calculus of Variations for Engineers, Third edition, 3rd Edition

Louis Komzsik
Algebraic and Stochastic Coding Theory

Algebraic and Stochastic Coding Theory

Dave K. Kythe, Prem K. Kythe

Publisher Resources

ISBN: 9781482253597