CHAPTER I - INTEGRAL EQUATIONS

Abstract

This chapter discusses integral equations. It presents some examples of the formation of integral equations. Any equation containing the required function under the integral sign is an integral equation. The chapter presents the classification of integral equations. It focuses on linear integral equations in which the required function has to be determined on the x axis. It also discusses Fredholm equations of the second kind, these being most commonly encountered in boundary value problems of mathematical physics. The theory of integral equations is much simpler for those of the second kind than for those of the first kind. The presence of the required function outside the integral sign leads naturally to the possibility of using the method of successive approximations. The chapter also highlights the properties of systems of orthogonal functions with certain remarks necessary for the discussion of integral equations. It reviews adjoint integral equation, degenerate equations, integral equations with unbounded kernels, integral equations with symmetric kernels, Volterra equation, and integral equations of the first kind and the second kind with Cauchy kernel.