Although Newton made his discoveries first, Leibniz actually published his work sooner. During their time, there was a lively debate over who deserves credit for discovering calculus. Due to the fact that Leibniz was the first to publish material on differential calculus, the notation and terminology we use today more closely resembles his than Newton's. So, in a nutshell, differential calculus deals with slope, change, and related applications. As is the case in differential calculus, approximations play an important role in the integral calculus.
People presently study calculus for a wide variety of reasons.
In a sense, calculus is the language of science. We use calculus to model dynamically changing quantities. Biologists, chemists, economists, engineers, and physicists all use calculus to study problems in their fields. Without calculus, it would be much harder to put satellites into orbit, build stable bridges, design efficient machinery, or prescribe appropriate drug doses. Page Tim Howard's Home Page CSU Math Dept.