# Fundamental Theorem of Calculus in Modern World Essay

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Updated: Jul 2nd, 2021

## Introduction

Despite the intentions of students to study all the necessary material during their courses, there are situations when they want to know how to use the offered information in real life. The fundamental theorem of calculus was developed by several mathematicians, including Bhaskara, Bernoulli, Barrow, and Leibniz, but the name of Isaac Newton is the one that is usually associated with calculus (Gautam 130). This essay aims to discuss the historical significance of Newton’s first calculus text and its application in the modern world.

## Sir Isaac Newton and the Formulation of the First Calculus Text

The contributions of Sir Isaac Newton are numerous in the fields of science, mathematics, and physics. He was an English mathematician, physician, and author of great scientific projects. The essence of the scientific revolution in the 17th century was considerably changed and improved, regarding his motion laws. The investigation of the composition of white light also was in the list of Newton’s discoveries.

He is known as the first one who applied calculus in physics when he worked on the development of the central properties of inversion. The works by Bernoulli and Barrow introduced the term “calculus” in the middle of the 17th century as “a particular method of calculation and mathematical study of continuous change” (Gautam 129). Newton produced the first calculus text that one antiderivative (indefinite integral) can be reversed by differentiation and obtained from a functional integral (Sohrab 279). Its worth is to connect algebraic indefinite integrals with analytic definite integral.

## Purpose and Historical Significance

The purpose of the fundamental theorem of calculus is to facilitate the integration process and promote the work of antiderivatives. There are many complex variables that can be defined in real calculus, and mathematicians must use complex integration to understand the need and progress of every variable. The significance of the theorem lies in the possibility to relate such processes as integration and differentiation and evaluate integrals in an easy way.

## Application

It is necessary to understand that the theorem of calculus can be applied in different spheres, including engineering, mechanics, physics, statistics, and even medicine. In his article, Monet defined calculus as the language of engineers, economists, and scientists and underlined its impact on daily activities. For example, in medicine, this theorem can be applied to investigate a bacterial culture. The growth of substances depends on a number of variables.

Differential calculus helps to combine the change in temperature and food sources and determine its relation to the rate of growth (Monet). In the field of engineering, calculus is used to plan long missions. Different orbiting velocities of the Earth and other gravitation influences should be identified (Monet). These manipulations are necessary to launch a probe in space flights.

Calculus may be used by modern business people and researchers in order to maximize their profits. Statisticians evaluate a variety of data that is taken from different sources. Calculus is effective to accurately predict possible answers to different questions and take the required actions. Chemistry is also the field where calculus is applied and influences the work of scientists. One of the common examples is the prediction of functions and rates of chemical reactions. Monet identified the information about the radioactive decay reaction as a significant step in modern life. Finally, the growth of graphic design activities increases the use of calculus in the field. The work with three-dimensional models requires much time and specific efforts. Calculus aims at determining the behaviors of models in changing conditions of a real environment, like movies or video games.

## Conclusion

In general, it is not always easy for students to understand why tutors make them learn multiple theories, theorems, and formulas. In the majority of cases, not much information is used in real life. However, the examples of calculus applications prove that even such a complex and unclear theorem may contribute to the development of different fields, including medicine, film industry, space flights, and business.

## Works Cited

Gautam, Pragati. “A Concise History of the Modern Calculus in Mathematics.” AKADEMOS, 2018, 129-143. Web.

Monet, Rahul. “Toppr. 2016. Web.

Sohrab, Houshang H. Basic Real Analysis. 2nd ed., Springer Science & Business Media, 2014.

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