Sunday, September 7, 2008

Calculus – The History

Calculus – The History
Calculus is a branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series. Basically, the calculus is the study of change and widespread applications in science and engineering and use to solve problems for which algebra is insufficient.

The calculus had its origin in the logical difficulties encountered by the ancient Greek mathematicians in their attempt to express their intuitive ideas in the ration or proportionalities of line, which vaguely recognized as continuous, in terms of numbers, which they regarded as discrete.

Indian mathematicians produced a number of works with some ideas of calculus. The formula for sum of the curve was first written by Aryabhata in 500AD, order to find the volume of a cube, which was an important step in the development of integral calculus.

The analysis of problems, together with the free use of the suggestive infinitesimal and the more extensive application on numerical concept, led within a short time to the algorithms of Newton and Leibniz, which constitute the calculus.

The ordinary questions of maxima and minima were amongst the first that engaged the attention of mathematician at the time of invention of the Differential or Fluxionary Calculus. This invention took place about the year 1684, three years before the memorable era of the publication of the Principia. But, the principles of the differential calculus, were not, like those of physical astronomy, given to the world, at once and as it were, on sudden, in a formal treatise.

The first problem relative to a species of maxima and minima distinct from the ordinary was proposed by Newton in the Principia; it was that of the solid of least resistance.

Newton actually discovered calculus between 1665 and 1667. At that time he was only 22 and preferred not to publish his discoveries. And the subject and doctrine became not matter of discussion and controversy, till John Bernoulli, Professor from Groningen wrote in the Leipsick Acts for June, 1696, required of mathematician the determination of the curve of quickest descent.

Gottfried Wilhelm Leibniz was the other inventor of calculus. During his time, he and Newton argued over ten ownerships of their discoveries, each staking a claim as the inventor of calculus. This dogfight eventually involved many prominent mathematicians all over Europe. The dispute later known as the “Great Sulk”

Although both were instrumental in its creation, they thought of the fundamental concept in very different ways. While Newton considered variables changing with time, Leibniz thought of variables x and y as ranging over sequences of infinitely close values. For Newton the calculus was geometrical while Leibniz took it towards analysis.
Calculus – The History
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