Shen, YefengThompson, Lina2023-08-182023-08-182023https://hdl.handle.net/1794/2873229 pagesThe subject of calculus covers a multitude of complex topics and labyrinthine worlds, but the commonality of studying rates of continuous change exists in all the subfields. Before the initial discoveries of calculus, math was very discrete. Often only standstill and countable objects could be studied which ruled out the examinations of millions of scenarios. Nowadays, it is argued that every single thing in the universe is constantly in motion (relative to some point), meaning there is no such thing as standstill. From this perspective, calculus can be applied to every single thing in the universe, and this beautiful idea can be exemplified throughout the existing diverse and frequent applications of calculus in modern-day society. There exists proof of ancient discoveries pioneering this advanced, modern subject of calculus; during those ancient times, mathematicians did not know that they were about to drastically change the world. These initial mathematical discoveries created a mass of extreme, influential curiosity within the subject of calculus and inspired future mathematicians to keep expanding it. Without calculus and its historical origins, we would have a hardly-advanced, primitive civilization today and extremely far less utilizations of mathematics. By starting with investigating the origins of calculus and then analyzing these roots in the modern applications, one can appreciate the marvelous growth, expansion, and essentiality of the subject.en-USCC BY-NC-ND 4.0HistoryApplicationsCalculusDifferentialIntegralThesis/Dissertation0009-0006-9487-4236