This handbook is addressed to students of technology institutf's where a
course on mathematical physics of relatively reduced volume is offered,
as well as to engineers and scientists. The aim of the handbook is to
treat (demonstrate) the basic methods for solving the simplest problems
of classical mathematical physics. The most basic among the methods
considered hrre i8 the superposition method. It allows one, based on
particular linearly indepmdent HolutionH (solution "atoms"), to obtain
the solution of a given problem. To that end the "Hupply" of solution
atoms must be complete. This method is a development of the well-known
method of particular solutions from the theory of ordinar '
differelltial equations. In contrast to the case of ordinary
differential equations, where the number of linearly independent
80lutions is always finite, for a linear partial differrntial equation a
complete "supply" of solution atoms is always infinite. This infinite
set of Holutions may be discrete (for example, for regular boundary
vahlP problems in a bounded domain), or form a continuum (for example,
in the case of problems in the whole space). In the first case the
superposition method reduces to tlH' construction of a series in the
indicated solution atoms with unknown coefficipnts, while in the second
case the series is replaced by an integral with respect to the corm:
iponding parameters (variables). This first step leads us to the general
solution of the associated hOlllogeneous equation under the assumption
that the set of solution atoms i;; "complete.
