ABSTRACT
The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as an active variable. This is achieved by means of the Laplace transformation. Problems where the spatial part of the domain is unbounded but the solution is not expected to decay fast enough away from the origin are particularly suited to this method. This chapter introduces a couple of useful mathematical entities related to the Laplace transformation. It examines the use of the Laplace transformation in the study of some typical linear mathematical models. Linear problems for equations that contain additional, lower-order terms can also be solved by the Laplace transformation method.
