Question: Consider the linear operator L[u] = () %3D

Consider the linear operator

that maps u(x) ˆˆ C1 to the vector-valued function whose components consist of the function and its first derivative.
(a) Compute the adjoint L* with respect to the L2 inner products on both the domain and target spaces, subject to the boundary conditions u(0) = u(1).
(b) Write down and solve the self-adjoint boundary value problem L* °L[u] = x - 1.

L[u] = (") %3D

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