«CALCULUS Исчисление» - Курсовая работа

Аннотация

Статья, которую я прочитала и перевела на русский язык, называется Исчисление. В тексте рассматриваются два раздела математического исчисления: дифференциальное и интегральное исчисление, подробно описывается их происхождение. Упоминаются имена известных ученых-физиков и математиков, проводивших исследования в данной области. Эта научная статья из учебно-методического комплекта «Macmillan Guide to Science», который опубликован в 2008 году. Статья предназначена для студентов, изучающих основы математики, а также - для каждой области науки и знания, таких как инженерное дело, медицина, экономика и бизнес.

Summary

The headline of the article I have read and translated is Calculus. This article deals with two divisions of calculus - differential and integral calculus. Their origin is described in detail. The names of famous physicists and mathematician researched in this field of science are noted. It is a scientific article from the teaching kit «Macmillan Guide to Science », which was published in 2008. The article is beneficial for students studying Mathematics and for every field of science and knowledge, such as engineering, medicine, economics and business.

Ключевые слова

Исчисление, дифференциальное и интегральное исчисление, скорость, длина, площадь, объем, предел.

Key words

Calculus, differential and integral calculus, rate, length, area, volume, limit.

Calculus

Calculus is the branch of mathematics that deals with the rates of change of quantities as well as the length, area and volume of objects. It grew out of geometry and algebra. There are two divisions of calculus - differential calculus and integral calculus. Differential calculus is the form concerned with the rate of change of quantities. This can be illustrated by slopes of curves. Integral calculus is used to study length, area and volume.

The earliest examples of a form of calculus date back to the ancient Greeks, with Eudoxus developing a mathematical method to work out area and volume. Other important contributions were made by the famous scientist and mathematician, Archimedes. In India, over the course of many years - from 500 AD to the 14th century - calculus was studied by a number of mathematicians. In fact, the first text on calculus was written in India. However, it was not until the end of the 1600s that calculus was taken up in Europe. There was much scientific activity at the time, and calculus was able to answer many questions, particularly in the field of physics. Many great mathematicians of the time embraced calculus and furthered its development, including Rene Descartes and Pierre de Fermat, but the most important contributions were made by Gottfried Leibniz and Isaac Newton. Newton was the first to use calculus in his studies of physics and Leibniz developed many of the symbols that we use in calculus.