History of Calculus

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Historyof Calculus

Calculuswas initially referred to as infinitesimal calculus it is amathematical discipline that focuses on derivatives, limits,functions, and infinite. Calculus is also referred to as themathematical study of change it contains three integral parts thatinclude integration, differentiation, and the relationship thatexists between two (integration and differentiation).Differentiation, mostly, deals with means of knowing the frequency ofalteration of a variable on other substances or time. On the otherhand, integration is concerned with the calculation of the amount orvolume of substances. The &quotNewton-Leibniz Formula&quot explainsthe relationship between differentiation and integration it furtherexplains that the two aspects are a reverse process of each other,under certain conditions [ CITATION Car59 l 1033 ].

Historyof Calculus

Thehistory of calculus refers to the historical development of thissubject from as early as ancient Greeks up to today. Ancient Greekswere the first people to discuss calculus concepts such as limits,infinity, and infinite partitions. Such concepts were very crucial inthe formulation of differentiation, integration, and the generaldevelopment of calculus mathematics. One of the great Greekphilosophers, Democritus, came up with the theory of atomic, andstated that the space was composed of very small atoms. The earliestChinese manuscript, Zhuangzi, stated that &quotwhen someone has arod, and they cut away a half per day, such an exercise can lastforever.” This Classics example shows how ancient humans used todescribe concepts like limits and infinity [ CITATION Edw79 l 1033 ].

Zenoraised the idea of infinite partitions by arguing that a man cannever catch up with the slowest turtle since whenever they make again in steps, the turtle will have already moved forward more stepsthus, living the man behind. Such an absurd observation paved way forancient humans to develop the concept of calculus in the subsequentyears.

Thedevelopment of calculus continued through the 17th century and 19thcentury, with different people contributing to its development.Mostly, the 17th century saw the contributions of Newton and Leibnizthe two major people credited with the most efforts in thedevelopment of calculus [ CITATION Car59 l 1033 ].

MajorPlayers of Calculus

Themajor players of calculus refer to the people who were responsiblefor its development. The first players in the development of calculusincluded the Greeks and the Chinese. The Greeks, under Democritus,were the first players to argue about the concept of calculus. Theydeveloped the idea before the 17th century, and were regarded as thefirst pioneers with regard to this subject. Zeno, also, helped peopleget clear imageries of the ideas of limits and infinity, by givingthe example of the man who could not reach a turtle through theapplication of the &quotinfinite partitions&quot. Archimedes alsoparticipated, as an ancient Greek, and was instrumental in showingthat certain areas could be calculated by dividing them intopartitions before summing the results. He paved way for today`scalculation of areas, by the concept of integration. This studyshows the ancient people gained knowledge on integration beforeknowing about differentiation [ CITATION Edw79 l 1033 ].

Thebreakthrough, for the development of calculus, came about whenLeibniz and Newton combined the two calculus ideas, differentiationand integration concept, through the theory of &quotFundamentalTheorem of Calculus&quot. This theory states that integration anddifferentiation refer to the reverse processes of each concept. Thedevelopment of this theory is regarded as the landmark in the growthof calculus, and it proved to useful as it was used in solvingproblematic challenges that simple math could not solve in theearlier years. For example, Jacob Bernoulli proved that the theory ofcalculus could be used in the calculation of logarithmic spirals.Some mathematicians, such as Rolle, opposed calculus because Newtonand Leibniz failed to find a firm logical foundation for the concept.Rolle was influential in the learning of elementary calculus, wherebyhe developed what became to be known as the Rolle`s Theorem. The 19thcentury saw mathematicians develop a logical foundation concerningcalculus, and they were able to thoroughly define some concepts suchas derivatives, integrals, and limits [ CITATION Ste90 l 1033 ].

Usesof Calculus in the Real World

Theconcept of calculus has many uses and applications in the real world.Many disciplines today use this concept, and they includeengineering, medicine, physics, economics, and statistics. Instudying physics, calculus is used to create a model in mathematicsto arrive at an optimal solution. Some concepts in physics requirecalculus to understand, and they include motion, heat, harmonics,astronomy, light, electricity, and dynamics. Moreover, Einstein`stheory of relativity also uses calculus in a calculation. The fieldof chemistry uses calculus in the prediction of functions thatinclude rates of reaction and radioactive decay. Birth and deathrates, in biology, also use calculus in their calculation. Ineconomics and business, calculus is used to calculate marginal costand revenue hence, enabling business people to predict profit orloss in their operations. Lastly, calculus is used in othermathematics disciplines such as statistics, algebra, and analyticalgeometry [ CITATION Car59 l 1033 ].

References

Boyer, C. B. (1959). The history of the calculus and its conceptual development : (The concepts of the calculus). New York: Dover.

Edwards, H. (1979). The historical development of the calculus. New York: Springer .

Hilger, S. (1990). Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus. Results in Mathematics, 18-56.