Fourier Analysis - Impacts of Mathematics on Other Educational Sciences

**Melita Štefan Trubić**, *University of Rijeka (Croatia)*

**Ines Radošević Medvidović**, *University of Rijeka (Croatia)*

Abstract

*Mathematics* is an essential tool for solving problems in many different areas, particularly those in engineering and *sciences* such as *physics, astronomy, and biology. Knowledge* of fundamental *mathematical laws enables students to be effective in research, discovery, and understanding of *scientific principles* in other areas. This fact is very important for m*athematics teachers and professors* at the faculty of engineering, civil engineering or a faculty of science. *Mathematical collegiums at these faculties are not only concerned with just pure mathematics with abstract concepts, but also with applied mathematics connected with the students’ future profession. However, a particular area of mathematics will be more attractive and understandable if its contents fit into the context of engineering or real scientific world problems. A very interesting mathematical field with a wide application in electronics, acoustics, and communications is the Fourier analysis, also known as spectral analysis. The Fourier analysis is the study of how functions can be decomposed into trigonometric or exponential functions. It was named after the French mathematician and physicist Jean Baptiste Joseph Fourier, who lived during the 18th and 19th centuries. He showed that a continuous periodic function can be expressed as an infinite sum of trigonometric or exponential functions with certain amplitudes, periods, and phases. This result, except for the function in the mathematical sense, had a significant impact on the understanding of the various areas that include oscillations and waves. Although the theory of Fourier series is complicated, the application of these series is rather simple and can be introduced already in high schools on the phenomenon of sound. Fourier integrals and Fourier transforms extended the ideas and techniques of the Fourier series to an arbitrary function that are not necessarily periodic. Since fast finite Fourier transforms are very useful for data compression on cell phones, disc drives, DVDs, and JPEGs, it can be stated that the Fourier analysis is present in our every day life, maybe without us even being aware of it. A whiff of the Fourier analysis and its fascinating application to other science education will be presented in this paper.

References: