Mathematics and Its History - Calculus - Coursework Example

Since Newton was a physicist, his thinking was influenced by physical matter and that is why he applied Calculus to try and explain physical phenomena. Since Leibniz was a Mathematician, Calculus to him was more of a statistical endeavor that required deep analysis.

However, both contributed greatly to the discovery and application of Calculus. Newton was responsible for developing the inverse relationship between the integral (area beneath a curve) and the derivative (slope of a curve). Leibniz’s work led him to discover the notations used for taking the integral and the derivative. When both of their work was combined, it led to the formation of Calculus.

This view was not always held and there was a dispute as to who, between the two men, actually discovered Calculus. Newton claimed that he had in 1666, at the age of 23, invented Calculus, when he had begun working on a technique known as fluents and fluxions. As for Gottfried, in 1675, due to his fascination with the tangent line, he began researching Calculus.

Even though Newton had discovered the principles of Calculus earlier on, he did not publish his findings, unlike Leibnitz who published his in 1684. Therefore, as a matter of public record, some deemed Leibnitz as the person who discovered the principles first. Consequently, this led to the Newton-Leibnitz controversy that continued to rage for centuries later. Newton’s Publication of Principia, in 1687, has also been a source of controversy since it is not entirely known whether he included his workings on Calculus. However, in a 1693 publication, he published part of his work on fluxion notation, but he fully published his work in 1704 (Jahnke 78).

Product Rule Controversy.

Newton seems to have been the one with the earliest breakthrough, but on his own, his work was incomplete. The adoption of Leibnitz notation is very instrumental in the existence of modern-day Calculus. Leibnitz's (dy/dx) notation is far better than Newton’s original version, which lacked a standard notation for differentiation and integration. This led to the eruption of disputes as to who developed the product rule. Certain factions stated that Leibnitz's notation and earlier publications proved that he was the founder, while other factions advocated for Newton, citing his earlier discovery of the Principles of Calculus.

Luckily, after both ideas were consolidated years later, Calculus was formed. It then began to be used to solve scientific conundrums that had puzzled scientists for a long time. Some of the problems that were solved include:-

1. Determining the absolute and relative extrema- minima and maxima.
2. Calculating the acceleration and velocity of an object when one is given a function that describes its position.
3. Determining the slope when given the tangent line to a curve from any point found on its length.
4. Determining the volume, surface area, and arc lengths of solids.
5. Designing the position of a function when given an object’s acceleration or velocity (Stillwell 98).