![]() It is irrelevant to this mathematical analysis. Thus, a mechanism is not an a priori condition for undertaking the analysis or for describing mathematically the data plot generated by Nature. and the data plot’s mathematical properties. How then would it be analyzed mathematically? This can be done in a systematic way using only the general D.E. Suppose there was a phenomenon of interest but no obvious mechanism on which to base a derivation of the function describing the data plot. Typically, these lead to either an algebraic function with its two empirical constants already assumed or a first-order D.E. This analysis technique departs significantly from others that may start with assumptions about the phenomenon’s mechanism, its variables, and empirical constants. and the unique solution function that describes the phenomenon’s behavior for the given boundary conditions. Practical examples of natural phenomena are analyzed to derive a specific D.E. Integrating yields the true empirical constants for the mathematical function as defined by the boundary conditions that uniquely describe the data plot. Its restrictive features reflect the essential requirements of dimensional analysis. The approach is new, unifying, and simple (Occam’s razor). that underlies the mathematical function describing each phenomenon’s data plot. The analysis uses the general underlying D.E., based on a dimensional analysis of the physical variables, together with the directly observable mathematical properties of the experimental data plot unique to the phenomenon. Thus, it focuses on the functional relationship of the variables that govern the phenomenon’s behavior, free of empirical constants. is also required to be free of empirical constants. The restriction places stringent requirements on the form of the D.E. describing a natural phenomenon reconcile the units of the terms on both sides of the D.E. A second-order differential equation (D.E.) free of these parameters can describe each, using only the variables. ![]()
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