Wave patterns

Kenisyn Mellema

First discovered by Jean-Baptiste Joseph Fourier, the Fourier series is a trigonometric series that expands periodic functions into a sum of sines and cosines, making it highly useful in analyzing functions and data that behave in a wave-like pattern. From heat diffusion to sound waves to digital image processing, the theoretical significance and real world applications of the Fourier series are incredibly widespread and far-reaching. This project focuses first on the utilization of Calculus concepts to define and analyze Fourier’s work and later moves to investigate it through the lens of computer science via python coding. The goal of this endeavor is to not only dive deeper into calculus, but to also build a bridge between current course material and future engineering applications. Taking the project a step further by using python to graph and model the result of this topical study allows for a valuable multidisciplinary learning experience that will also serve as a tool to aid in sharing and explaining the project. By approaching this subject from the perspective of an undergraduate student with little to no former knowledge of the topic, the desired result is to end with a deeper understanding of the Fourier series and the ability to convey- in language that is simple and easily accessible to students of any discipline- its significance and exciting applications.