First of all, a high school physics teacher's pendulum lesson could be justified via the application of convolutionary mathematical forms. However, the field would be far beyond the any high School student's abilitiy to comprehend. This is not to say that an abslolute genius wouldn't understand. Basically, convolution is a functional analysis using two distinct functions to produce a third function, which may be a modified version of one of the original functions.
The convolution can be defined for functions on groups other than Euclidean spaces. In particular, the circular convolution can be defined for periodic functions, ie , those function of the circle. And, the discrete convolution can be defined for functions on the set of counting number, ie integers. These generalizations of the convolution have applications in the field of numerical analysis and numerical algebra, and in the design of finite impulse response filter, ie signal processing.
An understanding of such would require at least four or five years of advanced college mathematics and some experience in the applications of several divergent fields.
