Integral equations play an important role for solving many different kinds of the mathematical physics and mechanics. In this book, we used four ways. The first way is to establish a mixed integral equations from the thermoelasticity problem, using the general fundamental equations, in the general form, with the aid of potential theory method. The second way is to discuss the existence and uniqueness of this new equation in view of pure mathematics using Picard method and Banach fixed point theorem when the Picard method fails. The third way, we used two different famous numerical methods:...