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. A functional is an expression that takes on a particular value that is dependent on the function used in the functional. The chapter shows that a broad class of functionals, the resulting boundary-value problem has the properties of being self-adjoint and positive definite. It presents a certain classes of functionals with the view of establishing necessary conditions for finding functions that extremize the functionals. The results were ordinary or partial differential equations for the extremal functions as well as the establishment of the dualities of kinematic and natural boundary conditions. The chapter presents the formulations for Euler-Lagrange equations and boundary conditions when there is only a single independent variable present.
