Calculus Case Study

Calculus is defined as, "The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus." (Oxford Dictionary). Contrary to any other type of math, calculus allowed Newton and other scientists to process the different motions and dynamic changes in world, such as the orbit of planets in space. Newton first became interested in the subject of mathematics while he was an undergraduate at Cambridge University. Although he did not focus on any of his math classes during his time as an undergraduate because it focused on Greek mathematics, he instead learned

Published as a book in 1736, Newton actually worked on his findings for some time until he finally finished in 1671, roughly 70 years earlier. In this book, Newton describes in the introduction that fluxions is a "method to resolve complex quantities into an infinite series of simple terms" along with twelve example problems that explain eight different ways to graph functions. This study initially began as a way to figure out how to solve and find the slope of a curve, whose slope was constantly varying, which could also be worded as "the slope of a tangent line to the curve at that point" (17th Century Mathematics - Newton). To solve, Newton calculated the derivative, f(x), in order to figure out the slope at any point of the function. This process of calculating the slope or derivative of a curve is called differential calculus, which is the method of fluxions. Depending on certain rules, derivative functions can be used such as sin(x), cos(x) for exponential, logarithmic, and trigonometric functions. This is done so that a derivative function can be stated without discontinuities for any curve. Once this is established, calculating the slope at any particular point on that curve is easy because any value could be inserted to x. This method can be applied; for example, if a person was in motion, the

He invented Calculus, this new form of math, in order to provide mathematical explanations to natural phenomena that he saw. Calculus is considered to demonstrate most vividly the direct connection between math and physics. Upon his discoveries, Newton was very hesitant in publishing his work because of his fear of the response and the controversy that it would cause. Because of this, most of his works were not published until after his death, like the Method of Fluxions. However, these publications allows people and other scientists to use his contributions that are very beneficial to used because to create new findings that we continue to use