ABSTRACT
This chapter describes that a procedure to find solutions of boundary value problems based on Green's functions and discusses some Jacques Charles Francois Sturm-Joseph Liouville boundary value problems that play an important role in physics applications. It presents Green's functions and their applications for self-adjoint differential operators of the second order. I. Newton's second law tells people that the sum of the forces acting upon the differential segment in both the horizontal and vertical directions is zero. The chapter considers self-adjoint differential operators of the second order for two reasons. First, all eigenvalues of a self-adjoint operator are real numbers and eigenfunctions corresponding to distinct eigenvalues are orthogonal. Second, a nonself-adjoint differential equation can be reduced to a self-adjoint counterpart. The chapter examines boundary value problems for scalar linear differential equations of the n-th order and their reformulations as first order systems.
