"calculus." Britannica Student Article “微积分” 大英百科学生文章

calculus 微积分

Britannica Student Library 大英百科学生文章

"calculus." Britannica Student Library from Encyclopædia Britannica 2007 Ultimate Reference Suite . (2007).

Introduction 介绍

The field of mathematics called calculus deals with change in processes or systems. In science many quantities change as we deal with them. The heat in a billet of steel begins to lessen the instant the billet is poured from molten metal. The number of bacteria in a culture changes measurably every fraction of a second. So, likewise, does the direction of a planet's motion in space as it speeds along its orbit around the sun.



In such instances we may want to know the rate of change. We may also want to know the rate as a basis for figuring the amount of change over a certain interval of space or time. The methods that solve these problems determine areas or volumes embraced within curved lines or surfaces—a calculation that often cannot be made with arithmetic or algebra.

The mathematical methods that have been devised for dealing with such problems make up calculus. Two mathematicians, Sir Isaac Newton of England and Gottfried Wilhelm Leibniz of Germany, share credit for independently developing calculus in the 17th century. The name, like the word calculate, is from the Latin term meaning “pebble,” from the ancient custom of using pebbles as counters in solving arithmetic problems. A simple example will illustrate some of the fundamental ideas and terms used in calculus.