A Brief History of Calculus
Calculus was created by Isaac Newton, a British scientist, as well as Gottfried Leibniz, a self-taught
German mathematician, in the 17th century. It has been long disputed who should take credit for
inventing calculus first, but both independently made discoveries that led to what we know now as
calculus. Newton discovered the inverse relationship between the derivative (slope of a curve) and
the integral (the area beneath it), which deemed him as the creator of calculus. Thereafter, calculus
was actively used to solve the major scientific dilemmas of the time, such as:
calculating the slope of the tangent line to a curve at any point along its length
determining the velocity and acceleration of an object given a function describing its
position, and designing such a position function given the object's velocity or acceleration
calculating arc lengths and the volume and surface area of solids
calculating the relative and absolute extrema of objects, especially projectiles
For Newton, the applications for calculus were geometrical and related to the physical world - such
as describing the orbit of the planets around the sun. For Leibniz, calculus was more about analysis
of change in graphs. Leibniz's work was just as important as Newton's, and many of his notations are
used today, such as the notations for taking the derivative and the integral.
Algebra and Geometry with Calculus
One of the earliest algebra topics learned is how to find the slope of a line--a numerical value that
describes just how slanted that line is. Calculus gives us a much more generalized method of finding
slopes. With it, we can find not only how steeply a line slopes, but indeed, how steeply any curve
slopes at any given point.
Without calculus, it is difficult to find areas of shapes other than those whose formulas you learned
in geometry. You may be able to find the area of commons shapes such as a triangle, square,
rectangle, circle, and even a trapezoid; but how could you find the area of the shape like the one
shown below?
