The idea of calculus was first introduced in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. It is still argued to this day who the real "father" of calculus is. Calculus is an ever expanding field with many applications extending into subjects one would otherwise not suspect to be affected. It's primary concerns deal with applications to engineering and physics. Derivatives and integrals are a main part which help with calculations of motion, space and time.
Calculus is the course reserved for those looking to get more involved with STEM field subjects and other subjects such as medicine. As the course progresses a student studies limits, derivative, integration, the behavior of functions including those from trigonometry and algebra. They will also be expected to find areas and volumes of figures and functions under different transformations. In college, calculus takes on a more theoretical approach with multiple variable calculus and differential equations. The applications of multiple variable extends deep into engineering with applications in fluid motion. Differential equations on the other hand lends an introduction to more serious analysis courses.