What Are the Amazing Facts about Calculus?
Calculus is a branch of mathematics that can be studied in two categories: differential and integral. Differential calculus involves calculating instantaneous rates of change, whereas integral calculus summates infinitely many small factors to determine some whole. Isaac Newton (England) and Gottfried Wilhelm Leibniz (Germany) are the two mathematicians who shared recognition (in the 17th century) for independently developing calculus. The name “calculus” was a Latin word used by the ancient Romans for a small stone in counting and gambling. Calculus, initially known as “the calculus of infinitesimals” or “infinitesimal calculus”, means the mathematical study of continuous change. Similarly, the study of various shapes is considered geometry, and the study of generalisations of mathematics operations (arithmetic operations) is considered algebra.
In mathematics schooling, calculus indicates courses in elementary mathematical analysis. This is mainly dedicated to studying functions and limits—also the continuity of functions to some extent. Calculus has become the primary entry topic for students who wish to study specialisations in other subjects besides mathematics, i.e., finance, economics, physics, chemistry, biology or actuarial science. Thus, students must study calculus carefully during their schooling, including all calculus fundamentals and related formulas. In higher education, they can understand calculus and its real-world applications.
The discovery of calculus and realising how to use calculus by humans took thousands of years. Yet, the invention of the current world using calculus arrived incredibly fast. The main reason is that calculus was a bridge for mathematicians with immense creations to use their ideas in the real world. Every new mathematician and physicist added to the facts and findings of prior scientists to make astonishing findings. Thus, calculus made it possible to solve problems as diverse as tracking the space shuttle’s position or forecasting the pressure produced behind a dam as the water rises. In addition, computers have become a beneficial tool for solving calculus problems that were once considered impossible.
The fundamental theorem of calculus is the main idea in calculus, which says that the two calculus techniques, differentiation and integration (differential and integral calculus), are inverses of each other. One can perform integration to undo a differentiation process and vice versa. This is similar to the arithmetics operations, where division is used to undo multiplication or subtraction to undo addition. In calculus, the process of finding derivatives of a function is called differentiation, whereas finding the integral of a function is referred to as integration. However, there exist different methods of performing differentiation and integration.
The applications of calculus in the real world are vast, some of which are known, and some are unknown. These applications can be studied separately for differential and integral calculus. Applications of differential calculus include calculations involving velocity, acceleration, the slope of a curve, etc. Applications of integral calculus include calculations involving area, volume, arc length, work, pressure, etc. Additionally, advanced applications of calculus include the power series and Fourier series. Calculus provides various tools, specifically the limit and the infinite series, that help in resolving paradoxes. It is also used to understand better the time, nature of space and motion.