Calculus is the branch of mathematics that analyzes aspects of change in processes or systems that can be modeled by functions. Through its two primary tools the derivative and the integral--it allows precise calculation of rates of change and of the total amount of change in such a system. The derivative and the integral grew out of the idea of a limit, the logical extension of the concept of a function over smaller and smaller intervals. Discovered in the late 17th century. independently by Issac Newton and G. Leibniz , calculus was one of the major scientific breakthroughs of the modern era.