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History of Calculus


Historical development of calculus can be traced to some period of time, that is ancient, medieval, and modern times. In the period from ancient times, some thoughts on the integral calculus has emerged, but not well developed and systematic. Calculation of volume and area of ​​which is the main function of the integral calculus can be traced back to the Egyptian Moscow papyrus (c. 1800 BC) in which the Egyptian pyramids to calculate volume beheaded. Archimedes developed this idea further and create heuristikyang resemble integral calculus.

In the Middle Ages, Indian mathematician, Aryabhata, using the concept of infinitely small in astronomical problems 499 and expressed in the form of the basic differential equations. This equation is then led Bhaskara II in the 12th century to develop an early form of derivative that represents a very small change in infinite and explain an early form of "Rolle's theorem". Around the year 1000, the Iraqi mathematician Ibn al-Haytham (Alhazen) was the first to derive a formula calculating the number of rank four, and by using mathematical induction, he developed a method to derive a general formula of the integral promotion is very important to the development of integral calculus .

In the 12th century, a Persian Sharaf al-Din al-Tusimenemukan derivative of the cubic function, an important result in differential calculus. In the 14th century, Madhava, along with the mathematician-astronomer from Kerala school of astronomy and mathematics, describes the special case of Taylor series, which is written in the text Yuktibhasa.

In modern times, independent discoveries occur at the beginning of the 17th century in Japan, by mathematicians such as Seki Kowa. In Europe, some mathematicians such as John Wallis danIsaac Barrow provide a breakthrough in the calculus. James Gregory proved a special case of the fundamental theorem of calculus in 1668.

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