Calculus, KAL kyuh luhs, is the branch of mathematics that deals with changing quantities. Students usually learn it in college after they have mastered algebra, geometry, and trigonometry.
Calculus is the language in which engineers, physicists, and other scientists develop theories and solve practical problems. For example, the laws of aerodynamics are expressed in terms of calculus. An airplane designer can use these laws to calculate the changing forces that affect an airplane during flight. Calculus has also stimulated many new directions in mathematics since its development in the 1600's.
Calculus was invented to answer questions that could not be solved using algebra or geometry. One branch of calculus, called differential calculus, began with questions about the speed of moving objects. For example, How fast does a stone fall two seconds after it has been dropped from a cliff? How fast is the earth moving around the sun on July 4? The other branch of calculus, integral calculus, was invented to answer a very different kind of question: What is the area of a shape with curved sides?
Although differential calculus and integral calculus began by solving different problems, their methods are closely related. The central problem of differential calculus is to find the rate at which a known, but varying, quantity changes. Integral calculus has just the reverse problem. It tries to find a quantity knowing the rate at which it is changing.
