ABSTRACT
This chapter focuses on the classical heat equation which is of the parabolic type. It reviews some leading principles of the integral Laplace transform and describes methods that can be used for obtaining compact representations of influence functions and matrices for the heat equation in one and two spatial variables. The chapter explores some basics of one of the classical integral transforms that is broadly used in applied mathematical physics. It focuses on the constructing procedure for obtaining influence matrices of an instant point heat source for the heat conduction phenomenon taking place in media whose conductive properties discontinuously vary with the spatial coordinates within the region. The chapter considers a single illustrative example just to demonstrate a possibility of constructing influence matrices of the heat equation for media whose conductive properties vary discontinuously with spatial variables within a region.
