Calculus

Definition & Facts

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Oct 10, 2023 - 22:31

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An illustration of the difference between average and instantaneous rates of changeThe graph of f(t) shows the secant between (t, f(t)) and (t + h, f(t + h)) and the tangent to f(t) at t. As the time interval h approaches zero, the secant (average speed) approaches the tangent (actual, or instantaneous, speed) at (t, f(t)).

calculus, branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Two mathematicians, Isaac Newton of England and Gottfried Wilhelm Leibniz of Germany, share credit for having independently developed the calculus in the 17th century. Calculus is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science. Calculus makes it possible to solve problems as diverse as tracking the position of a space shuttle or predicting the pressure building up behind a dam as the water rises. Computers have become a valuable tool for solving calculus problems that were once considered impossibly difficult.