Euler-Lagrange

Quote

In solving optimisation problems in function spaces, Euler made extensive use of this `method

of finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem of

finding extrema of a function to the problem of finding extrema of a function of n variables, and

then he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions can

be regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)

at different points), and the calculus of variations can be regarded as the corresponding analog of

differential calculus of functions of n real variables.