Application of the Laplace Transform in the Solution of Linear Integral Equations

Integral equations are defined and references are given to the Laplace transform technique. Most of the operations used are illustrated through a solution of Abel's integral equation. It is shown that the Liouville-Neumann series follows logically from an operational solution of Volterra's integral of the second kind. Whittaker obtained solutions to the integral equation with the kernel expressed in the last three forms. His procedure was quite involved and it is shown here that the same solutions are obtained more directly through the operational calculus based on the Laplace transform.