Calculus is the mathematical study of continuous change.

The two basic problems of calculus from a geometric point of view
are the tangent line problem and the area problem. The
first asks to find the slope of the tangent line to the graph of a
function at a given point. The second asks to find the area under the
graph of a function over a given interval.

The tangent line problem is solved by using an idea/calculation
called the derivative of the function. The area problem is
solved by using an idea/calculation called the integral of the
function. Essential to both the derivative and the integral is the
idea of a limit. Although initially it looks like derivatives
and integrals are extremely difficult to calculate and have nothing
to do with each other, it turns out that there are systematic methods
for calculating derivatives and integrals, and that they are
basically opposites of each other. The importance of calculus comes
from the enormous variety of applications for derivatives and
integrals beyond these motivating geometric ideas.

Calculus was invented in the 17th century by a number of people
(Isaac Newton being the best known) to solve
certain problems in physics. With calculus, the mathematical
description of the physical universe became possible for the first
time and modern science was born.

Throughout the 18th and 19th centuries calculus was used to
describe an enormous variety of physical phenomena from the motion of
planets to electromagnetic radiation, in many cases through the closely
related topic of differential equations. Today calculus remains at the
heart of the way we think of the physical world (science), our
methods for manipulating it (technology), and our language for describing
it (mathematics). As a result all students in science, engineering,
mathematics, and computer science are required to take a course in calculus.