HISTORY OF INFINITESIMAL CALCULUS

The problems that given beginnings to infinitesimal calculus, it's presented in Greek classical era (3rd century a. C.), but not found systematics methods of solution until after 20 centuries (17th century). The mathematicians lost fear that Greeks had the infinites: Kepler and Cavallieri were the first to use it; they took the way that would carry in half century to discovery of infinitesimal calculus.

Mid-17th century the infinitesimal quantities were used more each time to solve problems calculus tangents, areas, volumes; the first would give rise to differential calculus, the others to integral calculus. To end of 17th century Newton and Leibniz synthesized in two concepts, methods used by your predecessors, today we call “derivatives” and “integrals”. They develop rules to work the derivatives “derivation rules” and showed that both concepts were inverses “fundamental theorem of calculus”.

ISAAC NEWTON

In Cambridge England, developed his own method for tangent calculus, in 1665 he found an algorithm to derive functions algebraic, which coincide with the discovered by Fermat. In the end of 1665, he was dedicated to restructure bases of his calculus, and introduced the concept of “fluxion”, hat for he was the speed with a variable “flows” and “varies” with time.

GOTTFRIED LEIBNNIZ

He discovered and began to develop the differential calculus in 1675, was the first in publish the same results that newton discovered back 10 years. In his investigation conserved a geometric character, and difference to Newton, he treated to derivative as quotient incremental and no as a speed. He maybe was the greatest inventor of mathematics symbols and the names of: differential calculus and integral calculus, so symbols as “dx/dy” and “∫” for the derivative and the integral respectively. Was the first to use the term "function" and the symbol “=” for equality.

THE BERNOULLIS

Swiss brothers Jacques and jean made a great contribution for develop of calculus created by Leibniz, communicating with him through the mail. They formed almost everything that we know of differential calculus.

The diffusion of the new ideas was very slow and in the beginning their applications were limited. The new the new methods had each time more successful and allowed to solve many problems easily. The new achievements were subjected to hard criticisms, the justification and logical and rigorous explanations of the procedures used, not given until 19th century, when appeared other mathematicians, more worried with the final presentation of the methods that for utilization in solve concrete problems.

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