What are the Mathematical forms for non-ordinary differential equations that precede develop of the Beta - and Gamma - functions for a factorial analysis, closed range, subset circular,
'frozen in ...
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.
I find it hard to believe that the mathematics required to answer the question is needed at the high school level, but I'm not a Physics teacher. I hope the question was an honest one and not simply to show off. Jerry's response appeared to be "to the point", informed, and respectful. I am amazed at what I don't know and never even dreamed of its existence.
Meanwhile, Jerry's side bar re speed of light: Since darkness is the absence of light, wouldn't the speed of dark be the same as the speed of light?
Aha, yes Larry, you are correct in this analyis. The speed of dark can be said to be inversly proportionate to the speed of light. Congrats to you.