What is the adjoint linear operator and how do you find it?

[terryaki1016]

If L is the following first-order linear differential operator
L = p(x) d/dx
then determine the adjoint operator L* such that
integral from (a to b) [uL*(v) − vL(u)] dx = B(x) |from b to a|
What is B(x)?

sorry.. on my book there's only self-adjointness

i don't quiet understand what is the adjoint liear operator.

may someone solve this problem and tell me what exactly adjoint linear operator is ?

 

[Fredrik]

The adjoint $A^\dagger$ of a linear operator $A$ is defined by $\langle x,Ay\rangle=\langle A^\dagger x,y\rangle$. Physicists write the adjoint as $A^\dagger$, mathematicians write it as $A^*$. A is self-adjoint if $A^\dagger=A$.

 

[terryaki1016]

The adjoint $A^\dagger$ of a linear operator $A$ is defined by $\langle x,Ay\rangle=\langle A^\dagger x,y\rangle$. Physicists write the adjoint as $A^\dagger$, mathematicians write it as $A^*$. A is self-adjoint if $A^\dagger=A$.

how to find the A* then.. sry :(