Mathematical methodologies for the analysis and explanation of articulated and interconnected natural and man-made phenomena

Antonio Gallo, Gaetano La Bella

Mathematics is not merely a formal language, but an objective and critical tool for the analysis, interpretation and prediction of a variety of phenomena, both natural and man-made.

This contribution aims to define the value of applied mathematics in the field of scientific analysis, focusing on three fundamental mathematical methodologies: the derivative, the integral and the Fourier transform.

Each of these methodologies allows complex phenomena to be analysed through the analysis of particular trends and the decomposition into a summation of simpler functions, facilitating their interpretation and their complex, multidimensional and difficult to deal with as a whole.

Specifically, the derivative constitutes the cornerstone of infinitesimal analysis, the integral, on the other hand, defines the accumulation and summation of infinitesimal quantities, making it possible to derive overall information from the original data. Finally, the Fourier transform constitutes an indispensable tool for the frequency analysis of complex and variable systems. For each of these tools, a theoretical discussion has been provided accompanied by their use in practical activities, in order to document how their use can simplify and clarify the interpretation of complex hermetic phenomena.

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