Calculus is the mathematics of change. Differential calculus addresses the change of a function as one moves from point to point. A function u(x) is such that the dependent variable u takes on a unique value for each value of the independent variable x, and the derivative of the function at a point indicates the rate of change, or slope, at that point. In calculus of variations, we deal with the functional, which may be regarded as a “function of functions,” that is, a function that depends on other functions. More specifically, a functional is a definite integral whose integrand contains a function that is yet to be determined. A functional I[u(x)] is such that I takes on a unique scalar value for each function u(x). In Section 1.3, the travel time T[u(x)] and total energy E[u(z)] are functionals, which are functions of the path of light or the boat u(x) and bubble shape u(z), respectively. Variational calculus addresses the change in a functional as one moves from function to function. Accordingly, whereas differential calculus is the calculus of functions, variational calculus is the calculus of functionals.