ABSTRACT
This chapter presents methods to solve problems with three independent variables involving second-order differential equations and first-kind boundary conditions. Therefore, partial differential equations are involved. Mathematically, this class of cases can be summarized as first-kind boundary condition. The chapter considers the problem of a rectangular plate with prescribed temperatures at the borders for which the solution is obtained by separation of variables. It illustrates the relationship between dimensionless temperature profiles in a square plate against the dimensionless coordinates at three different dimensionless times.
