ABSTRACT
This chapter presents a view of elements of the theory of local extrema in order to set the stage for the introduction of the calculus of variations, which will be of considerable use in the ensuing studies of elastic structures. In place of the function of the preceding discussion authors are concerned with functionals, which are, plainly speaking, functions of functions. A procedure, forming one of the cornerstones of the calculus of variations, is considerably more complicated than the corresponding development in the calculus of functions, and authors undertake this in a separate section. Historically, the calculus of variations became an independent discipline of mathematics at the beginning of the 18th century. Much of the formulation of this mathematics was developed by the Swiss mathematician Leonhard Euler. It is instructive here to consider three of the classic problems that led to the growth of the calculus of variations.
