ABSTRACT
Integral equations are those equations in which the unknown function appears under the integral sign. Such equations have many applications in applied mathematics, physics, and engineering and more recently in economics and biology. One of the first integral equations to be investigated is due to Abel. He considered the case of a bead sliding down a frictionless wire and asked what the shape of the wire would be for the bead to slide from a given position, say (0, h), to a final position, say (x, 0), in a predetermined time, f(x) (see Fig. 11.1). He was led to the integral equation
FIGURE 11.1 Sliding of a bead.
