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The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz, but elements of it have appeared in ancient India, Greece, China, medieval Europe, and the Middle East. Calculus (plural calculi) is also used for naming some methods of calculation or theories of computation, such as propositional calculus, calculus of variations, lambda calculus, and process calculus. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Ĭalculus is a part of modern mathematics education. Today, calculus has widespread uses in science, engineering and economics. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz.
STOCHASTIC CALCULUS WITH INFINITESIMALS SERIES
Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.
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It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves) these two branches are related to each other by the fundamental theorem of calculus. Calculus (from Latin calculus, literally "small pebble used for counting") is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.