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Differential and Integral Calculus: How It Transformed the Face of Sciences from Physics to Economics
22 June، 2024
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Differential calculus is a branch of mathematics involving the concepts of differentiation and derivatives. Its evolution is closely tied with integral calculus, together forming the field known as calculus.

 

This discipline is fundamental to mathematical analysis, focusing on the study and discovery of functions through the calculation of derivatives and integrals.

 

Calculus examines phenomena involving changes in dimensions such as time, force, mass, length, and temperature. Essentially, it involves the study of rates of change.

 

 

Who is the inventor of calculus?

The development of calculus is attributed to two eminent scientists: Isaac Newton and Gottfried Wilhelm Leibniz. Each independently established the foundations of calculus, contributing essential concepts through different approaches.

 

Newton viewed calculus geometrically, while Leibniz advanced it towards analysis, recognizing the importance of developing suitable methods for handling calculus with multiple variables.

 

 

The Importance of Studying Calculus

The significance of calculus lies in its provision of a foundation for mathematical concepts. It aids in the development of scientific and engineering acumen and problem-solving skills.

 

Calculus techniques were developed to solve problems related to determining areas, volumes, and curve tangents.

 

Calculus holds substantial importance and wide application in both scientific and practical life. Here is how scientists utilize calculus across various fields:

 

In Physics:

Calculus is employed in the computations and definitions of concepts related to electricity, motion, acoustics, astronomy, light, and more.

 

Albert Einstein’s theory of relativity was built upon the principles of calculus.

 

In Chemistry:

Calculus is used to determine the rates of chemical reactions and essential information for radioactive decay re actions in radiochemistry.

 

In Biology:

It calculates birth and death rates and provides precise calculations of growth rates in bacterial colonies when variables such as temperature and food sources change.

In Economics:

 

Calculus is used to compute costs, revenues, and to determine maximum and minimum profits.

 

In Medicine:

Calculus measures blood flow, cardiac output, and helps in calculating appropriate drug dosages to ensure steady absorption rates, considering the dissolution rates of various drugs, and determining suitable dosages based on an individual’s height and weight.

 

It also assists in calculating the rates at which the human body metabolizes drugs.

 

 

Conclusion

Differential equations play a crucial role in our daily lives, aiding in the explanation of natural phenomena and the resolution of their problems.

 

They are instrumental in providing solutions to problems across various scientific fields.

 

Calculus has emerged as an indispensable tool in understanding our world, extending from the depths of space to the intricacies of daily life.

 

It offers the language and tools to analyze and solve problems in unprecedented ways, highlighting the importance of mathematics in developing our society and broadening our horizons of knowledge.

 

Undoubtedly, calculus will continue to inspire innovations and shape our future in unimaginable ways.

 

Author: Afaf Al-Dugheim, Mathematics Teacher at Masarat Initiative

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