Self-adjoint differential equations are defined by the condition that the inner product of two functions remains invariant under the differential operator. Specifically, for a differential operator T, it is self-adjoint if the equation (T^{\star}v,u)=(v,Tu) holds true. To convert a differential equation into a self-adjoint form, one must ensure that the differential operator satisfies this condition, which often involves manipulating the equation to align with the inner product definition provided.
PREREQUISITESMathematicians, physicists, and engineers interested in the theory and applications of differential equations, particularly those focusing on self-adjoint operators and their significance in various fields.