Calculus is a branch of mathematics that involves the study of rates of change. Before calculus was invented, all math was static: It could only help calculate objects that were perfectly still. But the universe is constantly moving and changing. No objects—from the stars in space to subatomic particles or cells in the body—are always at rest. Indeed, just about everything in the universe is constantly moving. Calculus helped to determine how particles, stars, and matter actually move and change in real time.
Calculus is used in a multitude of fields that you wouldn’t ordinarily think would make use of its concepts. Among them are physics, engineering, economics, statistics, and medicine. Calculus is also used in such disparate areas as space travel, as well as determining how medications interact with the body, and even how to build safer structures. You’ll understand why calculus is useful in so many areas if you know a bit about its history as well as what it is designed to do and measure.
There are two branches of calculus: differential and integral calculus. “Differential calculus studies the derivative and integral calculus studies…the integral,” notes the Massachusetts Institute of Technology. But there is more to it than that. Differential calculus determines the rate of change of a quantity. It examines the rates of change of slopes and curves.
This branch is concerned with the study of the rate of change of functions with respect to their variables, especially through the use of derivatives and differentials. The derivative is the slope of a line on a graph. You find the slope of a line by calculating the rise over the run.
Integral calculus, by contrast, seeks to find the quantity where the rate of change is known. This branch focuses on such concepts as slopes of tangent lines and velocities. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space or area under the curve. Integral calculus is used to figure the total size or value, such as lengths, areas, and volumes.