Relying on intuition and logic alone, it is not possible to achieve a deep understanding of the universe. A tool is needed that is capable of revealing simple patterns in complex and subtle natural phenomena. That mathematical tool is calculus. The development of calculus as a branch of mathematics is at the root of all scientific and technological advances in modern times. Without calculus, it is impossible to understand the behavior of gravity, the motion of the planets, the nature of light, electricity, or magnetism.

The development of calculus can trace its beginnings back to the time of the ancient Greeks. The mathematician Archimedes discovered formulas for determining the area and volume of geometric shapes such as cylinders and spheres. The methods he used were similar to the methods of today's integral calculus.

By the sixteenth and seventeenth centuries, the scientific revolution was in full swing and new...