A short introduction is given of direct variational methods and its relation to Galerkin and moment
methods, all flexible and powerful approaches for finding approximate solutions of difficult
physical equations. A pedagogical application of moment methods is given to the physically and
technically important Child–Langmuir law in electron physics. The analysis is shown to provide
simple, yet accurate, approximate solutions of the two-dimensional problem (a problem which does not
allow an exact analytical solution) and illustrates the usefulness and the power of moment methods.