The topic of the calculus of variations evolves from the analysis of functions. In the analysis of functions the focus is on the relation between two sets of numbers, the independent (x) and the dependent (y) set. The function f creates a one-to-one correspondence between these two sets, denoted as y = f(x).
In this chapter we generalize the concept of functions by allowing the members of the dependent set not being restricted to be numbers, but to be functions themselves. The relationship between these sets is now called a functional. The chapter will describe the fundamental problem of calculus of variations as finding extrema of functionals, most commonly formulated in the form of an integral. ...
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