Calculus of variations
How to find stationary values of functions of a single variable f (x), of several variables f (x, y, . . .) and of constrained variables, where x, y, . . . are subject to the n constraints gi(x, y, . . .) = 0, i = 1, 2, . . . , n will be known to the reader and is summarized in Sections A.3 and A.7 of Appendix A. In all those cases the forms of the functions f and gi were known, and the problem was one of finding the appropriate values of the variables x, y, etc.
We now turn to a different kind of problem in which we are interested in bringing about a particular condition for a given expression (usually maximizing or minimizing it) by varying the functions on which the expression depends. For instance, we might want ...