Functions of Complex Variables and their Usage in Real-World Applications
Jonas Ceviker
Honors Project: Functions of Complex Variables and their Usage in Real-World Applications
Honors Course: Honors College Algebra
Instructor: Mikhail Manilov
My name is Jonas Ceviker and I'm Currently pursuing an Associate in Arts, and an Associates in Sciences. I'm planning to transfer to UIUC in the fall of 2025 to Pursue my Undergraduate in Engineering at the Grainger School of Engineering. I'm interested in exploring various aspects of Engineering applications in both improving the infrastructure of cities as well as developing solutions that are climate friendly and sustainable. Although Math has never been my strong suit, Oakton and the Honors Program gave me the opportunity to work with professors to increase my knowledge and understanding of mathematics and learn to appreciate Math in a way that I previously had been unable to do. Working with Professor Manilov was a great experience. The professor and I worked closely, meeting nearly every day after my College Algebra class to review some of the research I had been conducting on Complex Variables, and it was through this work that I was able to develop a beginners understanding of applications within Statistics, Calculus, Physics, and other fields of STEM. Furthermore my research gave me the insight into understanding exactly how Complex Functions are utilized within Commercial, and Industrial Applications. This project, and my work with Professor Manilov ultimately inspired me to change my major and academic concentration to engineering and its various fields. The Honors Program is a way for students to work closely with their Professors and incentivizes a development of academic relationships that otherwise might've been overlooked. It is for this reason that I believe the Honors Program is an opportunity that every student should seek to explore, as it is a means to not only a deeper knowledge of any given subject but to also develop academic interests. Being able to participate in the Honors Program has been a pleasure and for lack of a better word, an honor.
In this paper, I introduce the Idea of complex variables and explore how they function as a means to provide solutions to functions that would otherwise have no real solutions. It is such that imaginary functions such which mathematically are known as complex functions provide an expansion to the model of mathematics that although is considered imaginary, ends up allowing for applications into theoretical mathematics, industry solutions, etc.
