The adjoint operator of the operator L(u) = xE0, 1] dx2 with boundary condition: u(1)= u(0), and u'(1)=2 u'(0), is L(v)= - d'v with boundary conditions dx? v(1)=2 v(0), and v(0)= v'(1). Ob. L(v)= with boundary conditions

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 20E
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du
xE0, 1]
The adjoint operator of the operator L(u)
%3D
dx
with boundary conditions u(1)= u(0), and u'(1)=2 u'(0),
is
O a
d'v
L(v)=
dx?
with boundary conditions
v(1)=2 v(0), and v (0)= v'(1).
d?v
with boundary conditions
Ob.
L(v)=
dx2
v(0) = 2 v(1), and v (0)= v'(1).
L(v) = -
d'v
with boundary conditions
dx
2 v(1) = v(0), and v (0) = v'(1).
L+(v) =
with boundary conditions
v(1) = v(0), and 2 v'(0)= v'(1).
%3D
dfv
L+(v) =
dx
with boundary conditions
V(1) = v(0), and v (0)=2 v' (1).
L(V) = -
dx
with boundary conditions
v(1) = v(0), and v (0) = 2 v'(1).
Transcribed Image Text:du xE0, 1] The adjoint operator of the operator L(u) %3D dx with boundary conditions u(1)= u(0), and u'(1)=2 u'(0), is O a d'v L(v)= dx? with boundary conditions v(1)=2 v(0), and v (0)= v'(1). d?v with boundary conditions Ob. L(v)= dx2 v(0) = 2 v(1), and v (0)= v'(1). L(v) = - d'v with boundary conditions dx 2 v(1) = v(0), and v (0) = v'(1). L+(v) = with boundary conditions v(1) = v(0), and 2 v'(0)= v'(1). %3D dfv L+(v) = dx with boundary conditions V(1) = v(0), and v (0)=2 v' (1). L(V) = - dx with boundary conditions v(1) = v(0), and v (0) = 2 v'(1).
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