Abstract
This chapter discusses the method of variation in problems with fixed boundaries. The methods of solving variational problems, that is, problems consisting of finding the maxima or minima of functionals, are very much like those of finding maxima or minima of ordinary functions. The variable z is called a function of a variable x, in writing z = f(x), if to each value of x from a certain domain, there corresponds a certain value of z, that is, to a given number x, there corresponds a number z. The variable v is called a functional depending on a function y (x), in writing v = v(y(x)), if to each function y(x), from a certain class of functions, there corresponds a certain value of v, that is, to a given function y(x), there corresponds a number v.
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