The branch of mathematics known as calculus serves as a natural and powerful tool for attacking a variety of problems that arise in physics, astronomy, engineering, chemistry, geology, biology, and other fields including, rather recently, some of the social sciences. It is reported that the Great pyramid of Egypt was built in 20 years. To model a conflict between two guerrilla armies, we assume that the rate that each one is put out of action is proportional to the product of the strengths of the two armies. These examples, chosen from various fields, illustrate some of the technical questions that can be answered by routine applications of calculus. But calculus is more than a technical tool - it is a collection of fascinating and exciting ideas that have interested thinking people for centuries.
Many people consider calculus to be one of the greatest achievements of the human intellect.
Inspired by problems in mechanics, Newton and Leibniz developed the ideas of calculus about 300 years ago. These concepts have to do with speed, area, volume, rate of growth, continuity, tangent line, and other concepts from a variety of fields. Calculus forces us to stop and think carefully about the meanings of the concepts. Another remarkable feature of the subject it its unifying power. Most of these ideas can be formulated so that they revolve around just two problems of a geometric nature.