About Calculus
The calculus consists of two main subjects: Differential Calculus and Integral Calculus.
Differential calculus arose from studying Fermat's tangent problem, which questions how to find the rate of change (or slope) at a point on a curve. The case is obvious for a line; the well-known formula for the slope of a line gives the rate of change at a point along the line. Newton and Leibniz, the originators of the calculus, demonstrated how to find the rate of change along a curve; this is the main question of differential calculus and its solution (derivatives) has a tremendous number of applications.
Integral Calculus was instigated by the area problem which questions how to find the area of a curved region. If for example, a region has a shape which can be approximated by a finite number of rectangles and/or triangles, then the area is obtained by arithmetic. However, the area of a bounded curved region can be much more difficult to approximate. Archimedes did attack such problems with his infamous "method of exhaustion", which defines a limiting process; an infinite process of approximating areas. The tangent problem and the area problem, as Newton and Leibniz demonstrated, are inverse problems and are systematically studied in the calculus along with many applications.
About Calculus
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/about-calculus.html
