Essay on History of Calculus

Calculus refers to a branch of Mathematics that involves derivatives and integrals of products to establish the rate of change. It is divided into differential and integral calculus which applies the concept of convergence of infinite series(Katz, 2003).The former involves properties, determination, and the use of differentials and derivatives while the latter deals with the application of integrals. Modern Calculus has widespread application in various sectors such as economics, engineering, and other sciences. It was developed in Europe in the 17th century by Gottfried Wilhelm and Isaac Newton but has also been found in China, Greece, Middle East, and Medieval Europe(Katz, 2003).

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The history of calculus goes as far as the ancient period in history in which some ideas leading to integral calculus were introduced unsystematically. Calculations of areas and volumes, an application of integral calculus, is available in the Egyptian Moscow Papyrus but is not accurate and the reasoning is not deductive(Katz, 2003). By the 8th century BC, India applied trigonometry with the rules of the chord and came up with cosine, sine, and tangent. Also, in Babylon, the scientists discovered the trapezoidal rule as the observed Jupiter astronomically. From 408-355 BC, the period of Greek Mathematics, exhaustion method was used in the calculation of volumes and areas which overcame the concept of limit(Katz, 2003). Archimedes developed these ideas more and invented heuristics which are similar to the integral calculus methods. In the Middle East, Alhazen came up with a formula for the addition of fourth powers which were used in integration. Later on, in the 14th century, some Indian mathematicians stated concepts of Infinite and Taylor series but could not combine different ideas under the integral and derivative components for problem-solving(Katz, 2003).

From the 17th century, mathematicians from Europe such as Pierre De Fermat came up with adequality method closely related to differentiation for determining tangents, minima, and maxima to some curves. Isaac Newton, one of the chief pioneers of calculus, later on, acknowledged that his ideas were inspired by De Pierres method of drawing tangents (Katz, 2003). On the integral component, Cavalieri came up with a method of indivisibles that was further developed by Torricelli and John Wallis. Isaac Barrow became the first person to prove the fundamental theorem of calculus fully (Katz, 2003). Isaac Newton and Gottfried Leibniz built on this network and independently came up with the theory of infinitesimal calculus still in the 17th century. Leibniz also developed useful and consistent concepts and notations while Isaac showed most of the important applications of integral calculus in geometry and physics. Newton saw calculus as a way of scientifically describing the generation of magnitudes and motion. On the other hand, Gottfrieds primary focus was on the tangent problem, and he believed that calculus was a metaphysical elaboration of change. Although both of them helped in the creation of a mathematical system of dealing with variable quantities, they had a different elementary base. There is controversy on who should be credited for inventing calculus. Isaac came up with the derivative function notation while Leibniz introduced the integral symbol and wrote dy/dx which are essential components of calculus.

Calculus helps in finding the impact of changing various conditions in a system. For instance, credit card companies apply calculus in setting the minimum payments on the cards statement as it is processed(Awen, Iber, & Iordyeh, 2010). It considers variables such as the available balance that is dynamic and the fluctuating interest rates. Therefore, calculus gives the human beings the power to control the material world.

References

Katz, V. (2003). Using the history of calculus to teach calculus. Science and Education, 2(3), 243-249. http://dx.doi.org/10.1007/bf00490066

Awen, E., Iber, M., & Iordyeh, F. (2010). Calculus of multivariate functions: its application in business. Journal of Research in National Development, 7(2). http://dx.doi.org/10.4314/jorind.v7i2.50974