# Essay on The Evolution of Differential Calculus

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Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight …show more content…
It is also used widely in physics and functional analysis.
Differential calculus is a topic that was first investigated by the Greeks, but has eventually evolved into a major concept studied by many mathematicians around the globe.
According to a Princeton University article, differential calculus is “the part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential.” As previously stated, differential calculus also focuses on instantaneous rates of change. The concept of the derivative began with the Greeks, which focuses on the core definition previously stated. The Greeks, more specifically Euclid, Archimedes, and Apollonius of Perga, investigated the idea of the tangent line around 300 B.C. They focused more on infinitesimals in order to study volume and areas. Infinitesimals were also used by the Indians to study the motion of the moon. In 1665, Sir Isaac Newton began to develop the study of differential calculus, but was forced to complete his studies at home due to the plague. According to Wise Greek, “In 1675, as Leibniz was creating differential calculus notations, he received two letters from Newton informing him of the work Newton had done in relation to calculus.” Leibniz was not aware of these