Mathematical analysis is a branch of mathematics that uses the concepts and methods common to the field of calculus. The key to mathematical analysis is the use of infinite processes; in turn, that involves passage to a limit, or, in other words, the basic branch of *calculus.* For example, a circle’s area can be thought of as the limiting value of the areas of regular polygons within the circle, as the number of the polygons’ sides increase indefinitely. The reason for calculus is simple: It is one of the most powerful and flexible tools not only in mathematics but in virtually every scientific field.