Which branch of mathematics primarily deals with rates of change?

Calculus is the branch of mathematics that primarily deals with rates of change. It focuses on understanding how quantities change with respect to one another, which is essential for analyzing dynamic systems in engineering, physics, and many other fields. One of the key concepts in calculus is the derivative, which measures the rate of change of a function at a particular point. This allows for the examination of how small changes in one variable can affect another variable, making it indispensable in fields that involve motion, growth, and optimization.

While statistics, geometry, and algebra all have their own important applications and principles, they do not center on the concept of rates of change in the same direct way that calculus does. Statistics focuses more on data analysis and interpretation, geometry studies shapes and the properties of space, and algebra deals with the manipulation of mathematical symbols and solving equations. Thus, when it comes to understanding and calculating rates of change, calculus is the definitive branch.