Calculus

Calculus is a branch of mathematics designed to find lengths, areas, and volumes and to study the rate of change of variable quantities called functions. Integral calculus uses the integral of a function to measure lengths, areas, and volumes, and differential calculus used the derivative of a function to study rates of change. Both are fundamental for any physical or social science dealing with changing quantities, for example, the velocity of a satellite or the profits of a corporation.

4,000 years ago, the Babylonians investigated areas and volumes, and more than 2,000 years ago, the Greek scientists Archimedes and Apollonius found areas and tangents for many curved figures. The French mathematician Rene Descarted combined the algebra inherited from medieval Muslim civilization with the geometry of the Greeks to produce analytic geometry, a method of solving geometric problems by using algebra and coordinate systems in 1637(Jeremy, 150-200). In 1665-66 the English scientist Isaac Newton, still a student, discovered the fundamental theorem of calculus, which shows the close connection between finding areas under curves and finding tangents to curves. He invented a general method that used this theorem and his discovery of the binomial theorem to solve many problems involving areas and tangents. With these discoveries, calculus was born.

Ten year later, the German mathematician Gottfried Leibniz independently made the same discoveries, and over the next 125 years mathematicians extended the theory of calculus to deal with quantities depending on many variables (Jeremy, 150-200). In 1734, a Swiss mathematician Leonhard Eular introduced an important step in calculus, partial derivatives of functions of several variables. Eular and other mathematicians, such as Jacques, Johann, and Daniel Bernoulli of Switzerland, and Pierre Laplace of France, applied calculus to problems in mechanics and probability. In early 19th century, the French mathematician A. L. Cauchy put calculus on a ...